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Orlicz-lacunary convergent triple sequences and ideal convergence

Yıl 2022, Cilt: 71 Sayı: 2, 581 - 600, 30.06.2022

Ömer Kişi Mehmet Gürdal

https://doi.org/10.31801/cfsuasmas.1027662
Cited By: 2

Öz

In the present paper we introduce and study Orlicz lacunary convergent triple sequences over n-normed spaces. We make an effort to present the notion of $g_{3}$-ideal convergence in triple sequence spaces. We examine some topological and algebraic features of new formed sequence spaces. Some inclusion relations are obtained in this paper. Finally, we investigate ideal convergence in these spaces.

Anahtar Kelimeler

Strongly almost convergence almost convergence n-norm g3-ideal convergence lacunary sequence Musielak-Orlicz function

Kaynakça

  • Alotaibi, A., Alroqi, A. M., Statistical convergence in a paranormed space, J. Ineq. Appl., 2012(1) (2012), 1-6. https://doi.org/10.1186/1029-242X-2012-39
  • Başar, F., Summability Theory and Its Applications, Bentham Science Publishers, İstanbul, 2012. https://doi.org/10.2174/97816080545231120101
  • Başarır, M., On some new sequence spaces, Riv. Math. Univ. Parma., 51 (1992), 339-347.
  • Başarır, M., Konca, Ş., Kara, E. E., Some generalized difference statistically convergent sequence spaces in 2-normed space, J. Ineq. Appl., 2013(177) (2013), 1-12. https://doi.org/10.1186/1029-242X-2013-177
  • Belen, C., Mohiuddine, S. A., Generalized weighted statistical convergence and application, Appl. Math. Comput., 219 (2013), 9821-9826. https://doi.org/10.1016/j.amc.2013.03.115
  • Bromwich, T. J., An Introduction to the Theory of Infinite Series, Macmillan and Co. Ltd., New York, 1965.
  • Connor, J. S., The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47-63. https://doi.org/10.1524/anly.1988.8.12.47
  • Das, G., Mishra, S. K., Banach limits and lacunary strong almost convergence, J. Orissa Math. Soc., 2(2) (1983), 61-70.
  • Das, G., Patel, B. K., Lacunary distribution of sequences, Indian J. Pure Appl. Math., 20(1) (1989), 64-74.
  • Das, G., Sahoo, S. K., On some sequence spaces, J. Math. Anal. Appl., 164 (1992), 381-398.
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Statistical convergence of complex uncertain triple sequence, Comm. Statist. Theory Methods, in press. https://doi.org/10.1080/03610926.2020.1871016
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Almost convergence of complex uncertain double sequences, Filomat, 35(1) (2021), 61–78. https://doi.org/10.2298/FIL2101061D
  • Das, B., Tripathy, B. C., Debnath, P., Nath, J., Bhattacharya, B., Almost convergence of complex uncertain triple sequences, Proc. Nat. Acad. Sci. India Sect. A, 91(2) (2021), 245-256. https://doi.org/10.1007/s40010-020-00721-w
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Characterization of statistical convergence of complex uncertain double sequence, Anal. Math. Phys., 10(4) (2020), 1-20. https://doi.org/10.1007/s13324-020-00419-7
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Study of matrix transformation of uniformly almost surely convergent complex uncertain sequences, Filomat, 34(14) (2021), 4907-4922. https://doi.org/10.2298/FIL2014907D
  • Duran, J. P., Infinite matrices and almost convergence, Math. Zeit., 128 (1972), 75-83.
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • Fridy, J. A., On statistical convergence, Analysis, 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301
  • Fridy, J. A., Orhan, C., Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43-51.
  • Gähler, S., 2-metrische Räume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115-148. https://doi.org/10.1002/mana.19630260109
  • Gähler, S., Linear 2-normietre rume, Math. Nachr., 28 (1965), 1-43. https://doi.org/10.1002/mana.19640280102
  • Gunawan, H., On n-inner product, n-norms and the Cauchy-Schwartz inequality, Sci. Math. Jpn., 5 (2001), 47-54.
  • Gunawan, H., Mashadi, M., On n-normed spaces, Int. J. Math. Sci., 27(10) (2001), 631-639. https://doi.org/10.1155/s0161171201010675
  • Gürdal, M., Şahiner, A., Statistical approximation with a sequence of 2-Banach spaces, Math. Comput. Modelling, 55(3-4) (2012), 471-479. https://doi.org/10.1016/j.mcm.2011.08.026
  • Gürdal, M., Şahiner, A., Açık, I., Approximation Theory in 2-Banach spaces, Nonlinear Anal., 71(5-6) (2009), 1654-1661.
  • Gürdal, M., Sarı, N., Savaş, E., A-statistically localized sequences in n-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(2) (2020), 1484-1497. https://doi.org/10.31801/cfsuasmas.704446
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-normed spaces, Southeast Asian Bull. Math., 33(2) (2009), 257-264.
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-banach spaces, Thai. J. Math., 2(1) (2004), 107-113.
  • Hardy, G. H., On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917) 86-95. https://doi.org/10.1112/plms/s2-1.1.124
  • Hazarika, B., Alotaibi, A., Mohiudine, S. A., Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput., 24(9) (2020), 6613-6622. https://doi.org/10.1007/s00500-020-04805-y
  • Kadak, U., Mohiuddine, S. A., Generalized statistically almost convergence based on the difference operator which includes the (p, q)-Gamma function and related approximation theorems, Results Math., 73(9) (2018), 1-31. https://doi.org/10.1007/s00025-018-0789-6
  • King, J. P., Almost summable sequences, Proc. Amer. Math. Soc., 17 (1966), 1219-1225. https://doi.org/10.1090/S0002-9939-1966-0201872-6
  • Konca, S., Başarir, M., Almost convergent sequences in 2-normed space and g-statistical convergence, J. Math. Anal., 4 (2013), 32-39.
  • Konca, Ş., Başarır, M., Generalized difference sequence spaces associated with a multiplier sequence on a real n-normed space, J. Ineq. Appl., 2013(335) (2013), 1-18. https://doi.org/10.1186/1029-242X-2013-335
  • Konca, Ş., Idris, M., Gunawan, H., A new 2-inner product on the space of p-summable sequences, J. Egyptian Math. Soc., 24 (2016), 244-249. https://doi.org/10.1016/j.joems.2015.07.001
  • Kostyrko, P., Macaj, M., Šalát, T., I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • Lindenstrauss, J., Tzafriri, L., On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390. https://doi.org/10.1007/BF02771656
  • Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167-190. https://doi.org/10.1007/BF02393648
  • Maddox, I. J., A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64.
  • Maddox, I. J., On strong almost convergence, Math. Proc. Phil. Soc., 85 (1979), 345-350. https://doi.org/10.1017/S0305004100055766
  • Misiak, A., n-inner product spaces, Math. Nachr., 140 (1989), 299-319. https://doi.org/10.1002/mana.19891400121
  • Mohiuddine, S. A., Alamri, B. A. S., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math., 113(3) (2019), 1955-1973. https://doi.org/10.1007/s13398-018-0591-z
  • Mohiuddine, S. A., Asiri, A., Hazarika, B., Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48(5) (2019), 492-506. https://doi.org/10.1080/03081079.2019.1608985
  • Mohiuddine, S. A., Hazarika, B., Alghamdi, M. A., Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560. https://doi.org/10.2298/FIL1914549M
  • Mohiuddine, S. A., Şevli, H., Cancan, M., Statistical convergence in fuzzy 2-normed space, J. Comput. Anal. Appl., 12(4) (2010), 787-798. https://doi.org/10.2298/FIL1204673M
  • Moricz, F., Rhoades, B. E., Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Cambridge Philos. Soc., 104 (1988), 283-294.
  • Mursaleen, M., Karakaya, V., Erturk, M., Gursoy, F., Weighted statistical convergence and its application to Korovkin type approximation theorem, Appl. Math. Comput., 218 (2012) 9132-9137. https://doi.org/10.1016/j.amc.2012.02.068
  • Mursaleen, M., Elements of Metric Spaces, Anamaya Publ., New Delhi, ISBN 81-88342-42-4, 2005.
  • Mursaleen, M., Başar, F., Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor & Francis Group, Series: Mathematics and Its Applications, Boca Raton London New York, ISBN 9780367819170, 2020.
  • Mursaleen, M., Edely, O. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223-231. https://doi.org/10.1016/j.jmaa.2003.08.004
  • Mursaleen, M., Generalized spaces of difference sequences, J. Math. Anal. Appl., 203 (1996), 738-745. https://doi.org/10.1006/jmaa.1996.0409
  • Nabiev, A., Pehlivan, S., Gürdal, M., On I-Cauchy sequences, Taiwanese J. Math., 11(2) (2007), 569-576.
  • Nath, J., Tripathy, B. C., Das, B., Bhattacharya, B., On strongly almost λ-convergence and statistically almost λ-convergence in the environment of uncertainty, Int. J. Gen. Syst., in press. https://doi.org/10.1080/03081079.2021.1998032
  • Parasher, S. D., Choudhary, B., Sequence spaces defined by Orlicz function, Indian J. Pure Appl. Math., 25 (1994), 419-428.
  • Patterson, R. F., Savaş, E., Lacunary statistical convergence of double sequences, Math. Commun., 10 (2005), 55-61. https://doi.org/10.1186/1029-242X-2014-480
  • Raj, K., Sharma, S. K., Applications of double lacunary sequences to n-norm, Acta Univ. Sapientiae Mathematica, 7 (2015), 67-88. https://doi.org/10.1515/ausm-2015-0005
  • Schaefer, P., Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104-110.
  • Şahiner, A., Gürdal, M., Düden, F. K., Triple sequences and their statistical convergence, Selçuk J. Appl. Math., 8(2) (2007), 49-55.
  • Şahiner, A., Tripathy, B. C., Some I-related properties of triple sequences, Selçuk J. Appl. Math., 9(2) (2008), 9-18.
  • Vulich, B., On a generalized notion of convergence in a Banach space, Ann. Math., 38(1) (1937), 156-174. https://doi.org/10.2307/1968517
  • Zeltser, M., Investigation of Double Sequence Spaces by Soft and Hard Analytical Methods, Diss. Math. Univ. Tartu, 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.

Yıl 2022, Cilt: 71 Sayı: 2, 581 - 600, 30.06.2022

Ömer Kişi Mehmet Gürdal

https://doi.org/10.31801/cfsuasmas.1027662
Cited By: 2

Öz

Kaynakça

  • Alotaibi, A., Alroqi, A. M., Statistical convergence in a paranormed space, J. Ineq. Appl., 2012(1) (2012), 1-6. https://doi.org/10.1186/1029-242X-2012-39
  • Başar, F., Summability Theory and Its Applications, Bentham Science Publishers, İstanbul, 2012. https://doi.org/10.2174/97816080545231120101
  • Başarır, M., On some new sequence spaces, Riv. Math. Univ. Parma., 51 (1992), 339-347.
  • Başarır, M., Konca, Ş., Kara, E. E., Some generalized difference statistically convergent sequence spaces in 2-normed space, J. Ineq. Appl., 2013(177) (2013), 1-12. https://doi.org/10.1186/1029-242X-2013-177
  • Belen, C., Mohiuddine, S. A., Generalized weighted statistical convergence and application, Appl. Math. Comput., 219 (2013), 9821-9826. https://doi.org/10.1016/j.amc.2013.03.115
  • Bromwich, T. J., An Introduction to the Theory of Infinite Series, Macmillan and Co. Ltd., New York, 1965.
  • Connor, J. S., The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47-63. https://doi.org/10.1524/anly.1988.8.12.47
  • Das, G., Mishra, S. K., Banach limits and lacunary strong almost convergence, J. Orissa Math. Soc., 2(2) (1983), 61-70.
  • Das, G., Patel, B. K., Lacunary distribution of sequences, Indian J. Pure Appl. Math., 20(1) (1989), 64-74.
  • Das, G., Sahoo, S. K., On some sequence spaces, J. Math. Anal. Appl., 164 (1992), 381-398.
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Statistical convergence of complex uncertain triple sequence, Comm. Statist. Theory Methods, in press. https://doi.org/10.1080/03610926.2020.1871016
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Almost convergence of complex uncertain double sequences, Filomat, 35(1) (2021), 61–78. https://doi.org/10.2298/FIL2101061D
  • Das, B., Tripathy, B. C., Debnath, P., Nath, J., Bhattacharya, B., Almost convergence of complex uncertain triple sequences, Proc. Nat. Acad. Sci. India Sect. A, 91(2) (2021), 245-256. https://doi.org/10.1007/s40010-020-00721-w
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Characterization of statistical convergence of complex uncertain double sequence, Anal. Math. Phys., 10(4) (2020), 1-20. https://doi.org/10.1007/s13324-020-00419-7
  • Das, B., Tripathy, B. C., Debnath, P., Bhattacharya, B., Study of matrix transformation of uniformly almost surely convergent complex uncertain sequences, Filomat, 34(14) (2021), 4907-4922. https://doi.org/10.2298/FIL2014907D
  • Duran, J. P., Infinite matrices and almost convergence, Math. Zeit., 128 (1972), 75-83.
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • Fridy, J. A., On statistical convergence, Analysis, 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301
  • Fridy, J. A., Orhan, C., Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43-51.
  • Gähler, S., 2-metrische Räume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115-148. https://doi.org/10.1002/mana.19630260109
  • Gähler, S., Linear 2-normietre rume, Math. Nachr., 28 (1965), 1-43. https://doi.org/10.1002/mana.19640280102
  • Gunawan, H., On n-inner product, n-norms and the Cauchy-Schwartz inequality, Sci. Math. Jpn., 5 (2001), 47-54.
  • Gunawan, H., Mashadi, M., On n-normed spaces, Int. J. Math. Sci., 27(10) (2001), 631-639. https://doi.org/10.1155/s0161171201010675
  • Gürdal, M., Şahiner, A., Statistical approximation with a sequence of 2-Banach spaces, Math. Comput. Modelling, 55(3-4) (2012), 471-479. https://doi.org/10.1016/j.mcm.2011.08.026
  • Gürdal, M., Şahiner, A., Açık, I., Approximation Theory in 2-Banach spaces, Nonlinear Anal., 71(5-6) (2009), 1654-1661.
  • Gürdal, M., Sarı, N., Savaş, E., A-statistically localized sequences in n-normed spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(2) (2020), 1484-1497. https://doi.org/10.31801/cfsuasmas.704446
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-normed spaces, Southeast Asian Bull. Math., 33(2) (2009), 257-264.
  • Gürdal, M., Pehlivan, S., The statistical convergence in 2-banach spaces, Thai. J. Math., 2(1) (2004), 107-113.
  • Hardy, G. H., On the convergence of certain multiple series, Proc. Camb. Phil. Soc., 19 (1917) 86-95. https://doi.org/10.1112/plms/s2-1.1.124
  • Hazarika, B., Alotaibi, A., Mohiudine, S. A., Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput., 24(9) (2020), 6613-6622. https://doi.org/10.1007/s00500-020-04805-y
  • Kadak, U., Mohiuddine, S. A., Generalized statistically almost convergence based on the difference operator which includes the (p, q)-Gamma function and related approximation theorems, Results Math., 73(9) (2018), 1-31. https://doi.org/10.1007/s00025-018-0789-6
  • King, J. P., Almost summable sequences, Proc. Amer. Math. Soc., 17 (1966), 1219-1225. https://doi.org/10.1090/S0002-9939-1966-0201872-6
  • Konca, S., Başarir, M., Almost convergent sequences in 2-normed space and g-statistical convergence, J. Math. Anal., 4 (2013), 32-39.
  • Konca, Ş., Başarır, M., Generalized difference sequence spaces associated with a multiplier sequence on a real n-normed space, J. Ineq. Appl., 2013(335) (2013), 1-18. https://doi.org/10.1186/1029-242X-2013-335
  • Konca, Ş., Idris, M., Gunawan, H., A new 2-inner product on the space of p-summable sequences, J. Egyptian Math. Soc., 24 (2016), 244-249. https://doi.org/10.1016/j.joems.2015.07.001
  • Kostyrko, P., Macaj, M., Šalát, T., I-convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • Lindenstrauss, J., Tzafriri, L., On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390. https://doi.org/10.1007/BF02771656
  • Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167-190. https://doi.org/10.1007/BF02393648
  • Maddox, I. J., A new type of convergence, Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64.
  • Maddox, I. J., On strong almost convergence, Math. Proc. Phil. Soc., 85 (1979), 345-350. https://doi.org/10.1017/S0305004100055766
  • Misiak, A., n-inner product spaces, Math. Nachr., 140 (1989), 299-319. https://doi.org/10.1002/mana.19891400121
  • Mohiuddine, S. A., Alamri, B. A. S., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math., 113(3) (2019), 1955-1973. https://doi.org/10.1007/s13398-018-0591-z
  • Mohiuddine, S. A., Asiri, A., Hazarika, B., Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48(5) (2019), 492-506. https://doi.org/10.1080/03081079.2019.1608985
  • Mohiuddine, S. A., Hazarika, B., Alghamdi, M. A., Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33(14) (2019), 4549-4560. https://doi.org/10.2298/FIL1914549M
  • Mohiuddine, S. A., Şevli, H., Cancan, M., Statistical convergence in fuzzy 2-normed space, J. Comput. Anal. Appl., 12(4) (2010), 787-798. https://doi.org/10.2298/FIL1204673M
  • Moricz, F., Rhoades, B. E., Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Cambridge Philos. Soc., 104 (1988), 283-294.
  • Mursaleen, M., Karakaya, V., Erturk, M., Gursoy, F., Weighted statistical convergence and its application to Korovkin type approximation theorem, Appl. Math. Comput., 218 (2012) 9132-9137. https://doi.org/10.1016/j.amc.2012.02.068
  • Mursaleen, M., Elements of Metric Spaces, Anamaya Publ., New Delhi, ISBN 81-88342-42-4, 2005.
  • Mursaleen, M., Başar, F., Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor & Francis Group, Series: Mathematics and Its Applications, Boca Raton London New York, ISBN 9780367819170, 2020.
  • Mursaleen, M., Edely, O. H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288 (2003), 223-231. https://doi.org/10.1016/j.jmaa.2003.08.004
  • Mursaleen, M., Generalized spaces of difference sequences, J. Math. Anal. Appl., 203 (1996), 738-745. https://doi.org/10.1006/jmaa.1996.0409
  • Nabiev, A., Pehlivan, S., Gürdal, M., On I-Cauchy sequences, Taiwanese J. Math., 11(2) (2007), 569-576.
  • Nath, J., Tripathy, B. C., Das, B., Bhattacharya, B., On strongly almost λ-convergence and statistically almost λ-convergence in the environment of uncertainty, Int. J. Gen. Syst., in press. https://doi.org/10.1080/03081079.2021.1998032
  • Parasher, S. D., Choudhary, B., Sequence spaces defined by Orlicz function, Indian J. Pure Appl. Math., 25 (1994), 419-428.
  • Patterson, R. F., Savaş, E., Lacunary statistical convergence of double sequences, Math. Commun., 10 (2005), 55-61. https://doi.org/10.1186/1029-242X-2014-480
  • Raj, K., Sharma, S. K., Applications of double lacunary sequences to n-norm, Acta Univ. Sapientiae Mathematica, 7 (2015), 67-88. https://doi.org/10.1515/ausm-2015-0005
  • Schaefer, P., Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104-110.
  • Şahiner, A., Gürdal, M., Düden, F. K., Triple sequences and their statistical convergence, Selçuk J. Appl. Math., 8(2) (2007), 49-55.
  • Şahiner, A., Tripathy, B. C., Some I-related properties of triple sequences, Selçuk J. Appl. Math., 9(2) (2008), 9-18.
  • Vulich, B., On a generalized notion of convergence in a Banach space, Ann. Math., 38(1) (1937), 156-174. https://doi.org/10.2307/1968517
  • Zeltser, M., Investigation of Double Sequence Spaces by Soft and Hard Analytical Methods, Diss. Math. Univ. Tartu, 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, Tartu, 2001.
Toplam 61 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Ömer Kişi 0000-0001-6844-3092

Mehmet Gürdal 0000-0003-0866-1869

Yayımlanma Tarihi 30 Haziran 2022
Gönderilme Tarihi 23 Kasım 2021
Kabul Tarihi 20 Ocak 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 71 Sayı: 2

Kaynak Göster

APA Kişi, Ö., & Gürdal, M. (2022). Orlicz-lacunary convergent triple sequences and ideal convergence. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(2), 581-600. https://doi.org/10.31801/cfsuasmas.1027662
AMA Kişi Ö, Gürdal M. Orlicz-lacunary convergent triple sequences and ideal convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2022;71(2):581-600. doi:10.31801/cfsuasmas.1027662
Chicago Kişi, Ömer, ve Mehmet Gürdal. “Orlicz-Lacunary Convergent Triple Sequences and Ideal Convergence”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, sy. 2 (Haziran 2022): 581-600. https://doi.org/10.31801/cfsuasmas.1027662.
EndNote Kişi Ö, Gürdal M (01 Haziran 2022) Orlicz-lacunary convergent triple sequences and ideal convergence. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 2 581–600.
IEEE Ö. Kişi ve M. Gürdal, “Orlicz-lacunary convergent triple sequences and ideal convergence”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 71, sy. 2, ss. 581–600, 2022, doi: 10.31801/cfsuasmas.1027662.
ISNAD Kişi, Ömer - Gürdal, Mehmet. “Orlicz-Lacunary Convergent Triple Sequences and Ideal Convergence”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/2 (Haziran 2022), 581-600. https://doi.org/10.31801/cfsuasmas.1027662.
JAMA Kişi Ö, Gürdal M. Orlicz-lacunary convergent triple sequences and ideal convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:581–600.
MLA Kişi, Ömer ve Mehmet Gürdal. “Orlicz-Lacunary Convergent Triple Sequences and Ideal Convergence”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 71, sy. 2, 2022, ss. 581-00, doi:10.31801/cfsuasmas.1027662.
Vancouver Kişi Ö, Gürdal M. Orlicz-lacunary convergent triple sequences and ideal convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(2):581-600.

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Journal of Uncertain Systems
https://doi.org/10.1142/S1752890923500034

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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