Araştırma Makalesi
BibTex RIS Kaynak Göster

Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions

Yıl 2024, Cilt: 12 Sayı: 1, 12 - 19, 28.01.2024

Gonca Durmaz Güngör İshak Altun

https://doi.org/10.36753/mathenot.1300609
Cited By: 1

Öz

By implying $\alpha $-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature.

Anahtar Kelimeler

Fixed point Right $K$-Cauchy sequence Quasi metric space $\alpha $ admissible

Kaynakça

  • [1] Boyd, D.W., Wong, J. S.W.: On nonlinear contractions. Proceedings of the American Mathematical Society. 20, 458-464 (1969).
  • [2] Ciric, Lj. B.: A generalization of Banach’s contraction principle. Proceedings of the American Mathematical Society. 45, 267-273 (1974).
  • [3] Hardy, G. E., Rogers, T. D.: A generalization of a fixed point theorem of Reich. Canadian Mathematical Bulletin. 16, 2021-206 (1973).
  • [4] Matkowski, J.: Fixed point theorems for mappings with a contractive iterate at a point. Proceedings of the American Mathematical Society. 62(2), 344-348 (1977).
  • [5] Zamfirescu, T.: Fix point theorems in metric spaces, Archiv der Mathematik. 23, 292-298 (1972).
  • [6] Alegre, C., Mar´ın, J., Romaguera, S.: A fixed point theorem for generalized contractions involving w-distances on complete quasi metric spaces. Fixed Point Theory and Applications. 2014, 1-8 (2014).
  • [7] Gaba, Y. U.: Startpoints and ( -)-contractions in quasi-pseudometric spaces, Journal of Mathematics. 2014, 8 pages (2014).
  • [8] Latif, A., Al-Mezel, S. A.: Fixed point results in quasimetric space. Fixed Point Theory and Applications. 2011, 1-8 (2011).
  • [9] Marın, J., Romaguera, S., Tirado, P.: Weakly contractive multivalued maps and w-distances on complete quasimetric spaces. Fixed Point Theory and Applications. 2011, 1-9 (2011).
  • [10] Marın, J., Romaguera, S., Tirado, P.: Generalized contractive set-valued maps on complete preordered quasi-metric spaces. Journal of Function Spaces and Applications. 2013, 6 pages (2013).
  • [11] Reilly, I. L., Subrahmanyam, P. V., Vamanamurthy, M. K.: Cauchy sequences in quasi- pseudo-metric spaces. Monatshefte für Mathematik. 93, 127-140 (1982).
  • [12] Romaguera, S.: Left K-completeness in quasi-metric spaces. Mathematische Nachrichten. 157, 15-23 (1992).
  • [13] Şimşek, H., Altun, İ.: Two type quasi-contractions on quasi metric spaces and some fixed point results. The Journal of Nonlinear Sciences and Applications. 10, 3777-3783 (2017).
  • [14] Şimsek, H., Yalcin, M. T.: Generalized Z-contraction on quasi metric spaces and a fixed point result. The Journal of Nonlinear Sciences and Applications. 10, 3397-3403 (2017).
  • [15] Altun, İ., Mınak, G., Olgun, M.: Classification of completeness of quasi metric space and some new fixed point results. Nonlinear functional analysis and applications. 371-384 (2017).
  • [16] Samet, B., Vetro, C., Vetro, P.: Fixed point theorems for 􀀀 -contractive type mappings. Nonlinear Analysis. 75, 2154-2165 (2012).
  • [17] Ali, M. U., Kamran, T., Shahzad, N.: Best proximity point for 􀀀 -proximal contractive multimaps. Abstract and Applied Analysis. 2014, 6 pages (2014).
  • [18] Altun, İ., Al Arifi, N., Jleli, M., Lashin, A., Samet, B.: A new concept of ( ; Fd)-contraction on quasi metric space.
  • The Journal of Nonlinear Sciences and Applications. 9, 3354-3361 (2016).
  • [19] Durmaz, G., Mınak, G., Altun, ˙I.: Fixed point results for 􀀀 -contractive mappings including almost contractions and applications. Abstract and Applied Analysis. 2014, 10 pages (2014).
  • [20] Hussain, N., Karapınar, E., Salimi, P., Akbar, F.: -admissible mappings and related fixed point theorems. Journal of Inequalities and Applications. 2013, 11 pages (2013).
  • [21] Hussain, N., Vetro, C., Vetro, F.: Fixed point results for -implicit contractions with application to integral equations. Nonlinear Analysis: Modelling and Control. 21(3), 362-378 (2016).
  • [22] Karapınar, E., Samet, B.: Generalized Alpha-Psi -contractive type mappings and related fixed point theorems with applications. Abstract and Applied Analysis. 2012, 17 pages (2012).
  • [23] Kumam, P., Vetro, C., Vetro, F.: Fixed points for weak 􀀀 -contractions in partial metric spaces. Abstract and Applied Analysis. 2013, 9 pages (2013).
  • [24] Jleli, M., Samet, B.: A new generalization of the Banach contraction principle. Journal of Inequalities and Applications. 2014, 1-8 (2014).
  • [25] Altun, İ., Hançer, H. A., Mınak, G.: On a general class of weakly Picard operators. Miskolc Mathematical Notes. 16(1), 25-32 (2015).
  • [26] Jleli, M., Karapinar, E., Samet, B.: Further generalizations of the Banach contraction principle. Journal of Inequalities and Applications. 2014(1), 1-9 (2014).

Yıl 2024, Cilt: 12 Sayı: 1, 12 - 19, 28.01.2024

Gonca Durmaz Güngör İshak Altun

https://doi.org/10.36753/mathenot.1300609
Cited By: 1

Öz

Kaynakça

  • [1] Boyd, D.W., Wong, J. S.W.: On nonlinear contractions. Proceedings of the American Mathematical Society. 20, 458-464 (1969).
  • [2] Ciric, Lj. B.: A generalization of Banach’s contraction principle. Proceedings of the American Mathematical Society. 45, 267-273 (1974).
  • [3] Hardy, G. E., Rogers, T. D.: A generalization of a fixed point theorem of Reich. Canadian Mathematical Bulletin. 16, 2021-206 (1973).
  • [4] Matkowski, J.: Fixed point theorems for mappings with a contractive iterate at a point. Proceedings of the American Mathematical Society. 62(2), 344-348 (1977).
  • [5] Zamfirescu, T.: Fix point theorems in metric spaces, Archiv der Mathematik. 23, 292-298 (1972).
  • [6] Alegre, C., Mar´ın, J., Romaguera, S.: A fixed point theorem for generalized contractions involving w-distances on complete quasi metric spaces. Fixed Point Theory and Applications. 2014, 1-8 (2014).
  • [7] Gaba, Y. U.: Startpoints and ( -)-contractions in quasi-pseudometric spaces, Journal of Mathematics. 2014, 8 pages (2014).
  • [8] Latif, A., Al-Mezel, S. A.: Fixed point results in quasimetric space. Fixed Point Theory and Applications. 2011, 1-8 (2011).
  • [9] Marın, J., Romaguera, S., Tirado, P.: Weakly contractive multivalued maps and w-distances on complete quasimetric spaces. Fixed Point Theory and Applications. 2011, 1-9 (2011).
  • [10] Marın, J., Romaguera, S., Tirado, P.: Generalized contractive set-valued maps on complete preordered quasi-metric spaces. Journal of Function Spaces and Applications. 2013, 6 pages (2013).
  • [11] Reilly, I. L., Subrahmanyam, P. V., Vamanamurthy, M. K.: Cauchy sequences in quasi- pseudo-metric spaces. Monatshefte für Mathematik. 93, 127-140 (1982).
  • [12] Romaguera, S.: Left K-completeness in quasi-metric spaces. Mathematische Nachrichten. 157, 15-23 (1992).
  • [13] Şimşek, H., Altun, İ.: Two type quasi-contractions on quasi metric spaces and some fixed point results. The Journal of Nonlinear Sciences and Applications. 10, 3777-3783 (2017).
  • [14] Şimsek, H., Yalcin, M. T.: Generalized Z-contraction on quasi metric spaces and a fixed point result. The Journal of Nonlinear Sciences and Applications. 10, 3397-3403 (2017).
  • [15] Altun, İ., Mınak, G., Olgun, M.: Classification of completeness of quasi metric space and some new fixed point results. Nonlinear functional analysis and applications. 371-384 (2017).
  • [16] Samet, B., Vetro, C., Vetro, P.: Fixed point theorems for 􀀀 -contractive type mappings. Nonlinear Analysis. 75, 2154-2165 (2012).
  • [17] Ali, M. U., Kamran, T., Shahzad, N.: Best proximity point for 􀀀 -proximal contractive multimaps. Abstract and Applied Analysis. 2014, 6 pages (2014).
  • [18] Altun, İ., Al Arifi, N., Jleli, M., Lashin, A., Samet, B.: A new concept of ( ; Fd)-contraction on quasi metric space.
  • The Journal of Nonlinear Sciences and Applications. 9, 3354-3361 (2016).
  • [19] Durmaz, G., Mınak, G., Altun, ˙I.: Fixed point results for 􀀀 -contractive mappings including almost contractions and applications. Abstract and Applied Analysis. 2014, 10 pages (2014).
  • [20] Hussain, N., Karapınar, E., Salimi, P., Akbar, F.: -admissible mappings and related fixed point theorems. Journal of Inequalities and Applications. 2013, 11 pages (2013).
  • [21] Hussain, N., Vetro, C., Vetro, F.: Fixed point results for -implicit contractions with application to integral equations. Nonlinear Analysis: Modelling and Control. 21(3), 362-378 (2016).
  • [22] Karapınar, E., Samet, B.: Generalized Alpha-Psi -contractive type mappings and related fixed point theorems with applications. Abstract and Applied Analysis. 2012, 17 pages (2012).
  • [23] Kumam, P., Vetro, C., Vetro, F.: Fixed points for weak 􀀀 -contractions in partial metric spaces. Abstract and Applied Analysis. 2013, 9 pages (2013).
  • [24] Jleli, M., Samet, B.: A new generalization of the Banach contraction principle. Journal of Inequalities and Applications. 2014, 1-8 (2014).
  • [25] Altun, İ., Hançer, H. A., Mınak, G.: On a general class of weakly Picard operators. Miskolc Mathematical Notes. 16(1), 25-32 (2015).
  • [26] Jleli, M., Karapinar, E., Samet, B.: Further generalizations of the Banach contraction principle. Journal of Inequalities and Applications. 2014(1), 1-9 (2014).
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Gonca Durmaz Güngör 0000-0002-5010-273X

İshak Altun 0000-0002-7967-0554

Erken Görünüm Tarihi 2 Kasım 2023
Yayımlanma Tarihi 28 Ocak 2024
Gönderilme Tarihi 22 Mayıs 2023
Kabul Tarihi 14 Ağustos 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Durmaz Güngör, G., & Altun, İ. (2024). Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions. Mathematical Sciences and Applications E-Notes, 12(1), 12-19. https://doi.org/10.36753/mathenot.1300609
AMA Durmaz Güngör G, Altun İ. Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions. Math. Sci. Appl. E-Notes. Ocak 2024;12(1):12-19. doi:10.36753/mathenot.1300609
Chicago Durmaz Güngör, Gonca, ve İshak Altun. “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”. Mathematical Sciences and Applications E-Notes 12, sy. 1 (Ocak 2024): 12-19. https://doi.org/10.36753/mathenot.1300609.
EndNote Durmaz Güngör G, Altun İ (01 Ocak 2024) Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions. Mathematical Sciences and Applications E-Notes 12 1 12–19.
IEEE G. Durmaz Güngör ve İ. Altun, “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”, Math. Sci. Appl. E-Notes, c. 12, sy. 1, ss. 12–19, 2024, doi: 10.36753/mathenot.1300609.
ISNAD Durmaz Güngör, Gonca - Altun, İshak. “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”. Mathematical Sciences and Applications E-Notes 12/1 (Ocak 2024), 12-19. https://doi.org/10.36753/mathenot.1300609.
JAMA Durmaz Güngör G, Altun İ. Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions. Math. Sci. Appl. E-Notes. 2024;12:12–19.
MLA Durmaz Güngör, Gonca ve İshak Altun. “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”. Mathematical Sciences and Applications E-Notes, c. 12, sy. 1, 2024, ss. 12-19, doi:10.36753/mathenot.1300609.
Vancouver Durmaz Güngör G, Altun İ. Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions. Math. Sci. Appl. E-Notes. 2024;12(1):12-9.

Cited By

Fixed point results for almost ($ \zeta -\theta _{\rho } $)-contractions on quasi metric spaces and an application
AIMS Mathematics
https://doi.org/10.3934/math.2024039
 Kapak Resmi İndir

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.