Research Article
BibTex RIS Cite

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

Year 2024, Volume: 12 Issue: 1, 12 - 19, 28.01.2024
https://doi.org/10.36753/mathenot.1300609

Abstract

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.

References

  • [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).
Year 2024, Volume: 12 Issue: 1, 12 - 19, 28.01.2024
https://doi.org/10.36753/mathenot.1300609

Abstract

References

  • [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).
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Gonca Durmaz Güngör 0000-0002-5010-273X

İshak Altun 0000-0002-7967-0554

Early Pub Date November 2, 2023
Publication Date January 28, 2024
Submission Date May 22, 2023
Acceptance Date August 14, 2023
Published in Issue Year 2024 Volume: 12 Issue: 1

Cite

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. January 2024;12(1):12-19. doi:10.36753/mathenot.1300609
Chicago Durmaz Güngör, Gonca, and İshak Altun. “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”. Mathematical Sciences and Applications E-Notes 12, no. 1 (January 2024): 12-19. https://doi.org/10.36753/mathenot.1300609.
EndNote Durmaz Güngör G, Altun İ (January 1, 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 and İ. Altun, “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”, Math. Sci. Appl. E-Notes, vol. 12, no. 1, pp. 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 (January 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 and İshak Altun. “Some Fixed Point Results for $\alpha $-Admissible Mappings on Quasi Metric Space Via $% \theta $-Contractions”. Mathematical Sciences and Applications E-Notes, vol. 12, no. 1, 2024, pp. 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.

20477

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