Coincidence of Fixed Points with Mixed Monotone Property
Main Article Content
Abstract
The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result.
Received 30/10/2021
Accepted 5/4/2022
Published Online First 20/9/2022
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
References
Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundam Math . 1922; 3(1): 133–181.
Dass BK, Gupta S. An extension of Banach contraction principle through rational expression. Indian J. Pure Appl. Math. 1975; 6(1975): 1455–1458.
Jaggi DS. Some unique fixed point theorems. Indian J. Pure Appl. Math. 1977; 8(2): 223–230.
Ran AC, Reurings MC. A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc Am Math Soc. 2004; 132(5): 1435–1443.
Rao GV, Sri YV. A Common Fixed Point Theorems for Generalized Contraction Mappings and Partially and Ordered Metric Spaces. J Phys Conf Ser. 2019; 1172: 012111.
Rao NS, Kalyani K, Kejal K. Contractive mapping theorems in Partially ordered metric spaces. CUBO. 2020; 22(2): 203–214.
Eke KS, Oghonyon JG. Some fixed point theorems for rational-type contractive maps in ordered metric spaces. Int J Math Comput Sci. 2020; 15(1): 65-72.
Bhaskar TG, Lakshmikantham V. Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal Theory Methods Appl. 2006; 65(7): 1379-1393.
Kalyani K, Rao NS. Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces. CUBO. 2021; 23(2): 207–224.
Rao NS, Kalyani K. Coupled fixed point theorems with rational expressions in partially ordered metric spaces. J Anal. 2020; 28(4): 1085–1095.
Rao NS, Kalyani K. Generalized contractions to coupled fixed point theorems in partially odered metric spaces. J Siberian Fed Univ Math Phys. 2020; 23(4): 492–502.
Gupta V, Mani N, Jindal J. Some new fixed point theorems for generalized weak contraction in partially ordered metric spaces. Comp Math Methods. 2020; 2(5): 1-9.
Ćirić L, Lakshmikantham V. Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces. Stoch Anal Appl. 2009; 27(6): 1246–1259.
Arab R, Rabbani M. Coupled coincidence and common fixed point theorems for mappings in partially ordered metric spaces. Math. Sci Lett. 2014; 3(2): 81–87.
Luaibi HH, Abed SS. Fixed point theorems in general metric space with an application. Baghdad Sci J. 2021; 18(1(Suppl. March)): 812-815.
Ajeel YJ, Kadhim SN. Some Common fixed points theorems of four weakly compatible mappings in metric spaces. Baghdad Sci J. 2021 February; 18(3): 543-546.
Hashim AM, Abd Zaid A. Fixed point results for multivalued mappings in partial Hausdorff metric spaces. Basrah J. Sci. 2020 ; 38(3): 373-386.
Rao NS, Kalyani K. On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces. Sahand Commun Math Anal. 2021; 18(1): 123-136.
Rao NS, Kalyani K. Unique fixed point theorems in partially ordered metric spaces, Heliyon. 2020; 6(11): 7. https://doi.org/10.1016/j.