Some fixed point results in rectangular metric spaces
Main Article Content
Abstract
After motivation from Geraghty-type contractions and of Farhan, et al. we define α-admissible mappings and demonstrate the fixed point theorems for the above-mentioned contractions in rectangular metric space in this study. In the end, we discuss some consequences of our results as corollaries.
2010 MSC: 47H10, 54H25.
Downloads
Article Details
Copyright (c) 2023 Devi S, et al.

This work is licensed under a Creative Commons Attribution 4.0 International License.
Akbar F, Khan AR. Common fixed point and approximation results for noncommuting maps on locally convex spaces. Fixed Point Theory Appl. 2009; 207503.
Farhana A, Peyman S, Nawab H. α-admissible mappings and related fixed point theorems. Journal of Inequalities and Applications. 2013; 2013:114.
Aydi H, Karapinar E, Erhan I. Coupled coincidence point and coupled fixed point theorems via generalized Meir-Keeler type contractions. Abstr Appl Anal. 2012; 781563.
Aydi H, Karapinar E, Shatanawi W, Tripled common fixed point results for generalized contractions in ordered generalized metric spaces. Fixed Point Theory Appl. 2012; 101.
Aydi H, Vetro C, Karapinar E. Meir-Keeler type contractions for tripled fixed points. Acta Math Sci. 2012; 32(6):2119-2130.
Aydi H, Vetro C, Sintunavarat W, Kumam P. Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces. Fixed Point Theory Appl. 2012; 124.
Berinde V. Approximating common fixed points of noncommuting almost contractions in metric spaces. Fixed Point Theory. 2010; 11(2):179-188.
Berinde V. Common fixed points of noncommuting almost contractions in cone metric spaces. Math Commun. 2010; 15(1): 229–241.
Berinde V. Common fixed points of noncommuting discontinuous weakly contractive mappings in cone metric spaces. Taiwan J Math. 2010; 14(5): 1763-1776.
Branciari A. A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces. Publicationes Mathematicae Debrecen. 2000; 57(1-2): 31-37.
Victor B. Metric spaces: iteration and application”, Cambridge University Press. ISBN 0-521-31897-1, 1985.
Ciric L, Abbas M, Saadati R, Hussain N, Common fixed points of almost generalized contractive mappings in ordered metric spaces. Appl Math Comput. 2011; 217: 5784-5789.
Ciric L, Hussain N, Cakic N. Common fixed points for Ciric type f -weak contraction with applications. Publ Math (Debr.). 2010; 76(1–2): 31-49.
Ciric LB. A generalization of Banach principle. Proc Am Math Soc. 1974; 45: 727-730.
Edelstein M. On fixed and periodic points under contractive mappings. J Lond Math Soc. 1962; 37: 74–79.
Fulga A. On interpolative contractions that involve rational forms. Adv Difference Equ. 2021; 448: 12.
George A, Veeramani P. On some results in fuzzy metric spaces. Fuzzy sets and systems. 1994; 64: 395-399.
Harjani J, Sadarangani K. Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 2009; 71: 3403-3410.
Hussain N, Berinde V, Shafqat N. Common fixed point and approximation results for generalized ϕ –contractions. Fixed Point Theory. 2009; 10: 111-124.
Hussain N, Cho YJ. Weak contractions, common fixed points, and invariant approximations. J Inequal Appl. 2009: 390634.
Hussain N, Jungck G. Common fixed point and invariant approximation results for noncommuting generalized (f,g)-nonexpansive maps. J Math Anal Appl. 2006; 321: 851-861.
Hussain N, Khamsi MA, Latif A. Banach operator pairs and common fixed points in hyperconvex metric spaces. Nonlinear Anal. 2011; 74: 5956-5961.
Hussain N, Khamsi MA. On asymptotic pointwise contractions in metric spaces. Nonlinear Anal. 2009; 71: 4423-442.
Karapinar E, Fulga A. New Hybrid Contractions on b-Metric Spaces. Mathematics. 2019; 7(7): 15.
Karapinar E. Revisiting the Kannan Type Contractions via Interpolation. Adv Theory Nonlinear Anal Appl. 2018; 2(2):85-87.
Mutlu A, Gürdal U, Ozkan K. Fixed point results for α−ψ contractive mappings in bipolar metric spaces. Journal of Inequalities and Special Functions. 2020; 11: 64-75.
Mutlu A, Gürdal U, Ozkan K. Fixed point theorems for multivalued mappings on bipolar metric spaces. Fixed Point Theory. 2020; 21: 271-280.
Samet B, Vetro C, Vetro P. Fixed point theorem for α−ψ contractive type mappings. Nonlinear Anal. 2012; 75: 2154–2165.