Fixed point theorem for Nonlinear $\theta-\phi-$contraction via $w-$distance
DOI:
https://doi.org/10.20956/j.v19i1.20866Keywords:
Fixed point, Nonlinear $\theta-\phi-$contraction, $w-$distance, ntegral equation.Abstract
This paper is aimed to the notion of $\theta-\phi-$contraction defined on a metric space with $w-$distance. Moreover, fixed point theorems are given in this framework. Some illustrative examples are provided to advocate the usability of our results.
As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations.
References
bibitem{ALG} C. Alegre, J. Marín, S. Romaguera, A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces. Fixed Point Theory Appl 2014, 40 (2014).
bibitem{BAN} S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., $3, (1922), 133-181.$
bibitem{KADA} O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44, (1996), 381–391.
bibitem{KIR} W. A. Kirk, N. Shahzad, Generalized metrics and Caristi’s theorem. Fixed Point Theory Appl 2013, 129 (2013).
bibitem{KRI} A. Kari, M. Rossafi, E. Marhrani, M. Aamri, $theta-phi-$contraction on $(alpha,eta)-$complete rectangular $b-$metric spaces, International Journal of Mathematics and Mathematical Sciences, vol. 2020, Article ID 5689458, 9 pages, 2020. https://doi.org/10.1155/2020/5689458
bibitem{KA1} A. Kari, M. Rossafi, E. Marhrani, M. Aamri, New Fixed Point Theorems for $theta-phi-$contraction on complete rectangular $b-$metric spaces, Abstract and Applied Analysis, vol. 2020, Article ID 8833214, 12 pages, 2020. https://doi.org/10.1155/2020/8833214
bibitem{KAR} A. Kari, M. Rossafi, E. Marhrani, M. Aamri, Fixed-Point Theorem for Nonlinear $ F $-Contraction via $ w$-Distance, Advances in Mathematical Physics, vol. 2020, Article ID 6617517, 10 pages, 2020. https://doi.org/10.1155/2020/6617517
bibitem{KA3} A. Kari, M. Rossafi, H. Saffaj, E. Marhrani, M. Aamri, Fixed-Point Theorems for $ theta-phi $-Contraction in Generalized Asymmetric Metric Spaces, International Journal of Mathematics and Mathematical Sciences, vol. 2020, Article ID 8867020, 19 pages, 2020. https://doi.org/10.1155/2020/8867020
bibitem{PIRI1} H. Piri, P. Kumam, Wardowski type fixed point theorems in complete metric spaces. Fixed Point Theory Appl 2016, 45 (2016).
bibitem{PIRI} H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces. Fixed Point Theory Appl. 2014, 210 (2014).
bibitem{JS} M. Jleli, E. Karapinar, B. Samet, Further generalizations of the Banach contraction principle. J. Inequal. Appl. 2014, Article ID 439 (2014).
bibitem{WONG} T. Wongyat, W. Sintunavarat, The existence and uniqueness of the solution for nonlinear Fredholm and Volterra integral equations together with nonlinear fractional differential equations via w-distance. Adv Differ Equ 2017, 211 (2017).
bibitem{ZH} D. Zheng , Z. Cai , P. Wang, New fixed point theorems for $ (theta,phi )$-contraction in complete metric spaces.J. Nonlinear Sci. Appl., 10, (2017), 2662-2670.
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This work is licensed under a Creative Commons Attribution 4.0 International License.
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