Mathematics and Statistics Vol. 8(4), pp. 382 - 387
DOI: 10.13189/ms.2020.080402
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Common Coupled Fixed Point Theorems for Weakly F-contractive Mappings in Topological Spaces

Savita Rathee ¹, Priyanka Gupta ^2,*
1 Department of Mathematics, Maharshi Dayanand University, Rohtak-124001, Haryana, India
² Department of Mathematics, Pt. Chiranji Lal Sharma Govt. P.G. College, Karnal-132001, Haryana, India

ABSTRACT

In late sixties, Furi and Vignoli proved fixed point results for α-condensing mappings on bounded complete metric spaces. Bugajewski generalized the results to "weakly F-contractive mappings" on topological spaces(TS). Bugajeski and Kasprzak proved several fixed point results for "weakly F-contractive mapping" using the approach of lower(upper) semi-continuous functions. After that, by modifying the concept of "weakly F-contractive mappings", the coupled fixed point results were proved by Cho, Shah and Hussain on topological space. On different spaces, common coupled fixed point results were discussed by Liu, Zhou and damjanovic, Nashine and Shatanawi and many other authors. In this work, we prove the common coupled fixed point theorems by adopting the modified definition of weakly F-contractive mapping r : T→T; where T is a topological space. After that, we extend the result of Cho, Shah and Hussain for Banach spaces to common coupled quasi solutions enriched with a relevant transitive binary relation. Also, we give an example in the support of proved result. Our results extend and generalize several existing results in the literature.

KEYWORDS
Topological Space, Weakly F-contractive Mapping, Common Coupled Fixed Point, Relatively Compact Set

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Savita Rathee , Priyanka Gupta , "Common Coupled Fixed Point Theorems for Weakly F-contractive Mappings in Topological Spaces," Mathematics and Statistics, Vol. 8, No. 4, pp. 382 - 387, 2020. DOI: 10.13189/ms.2020.080402.

(b). APA Format:
Savita Rathee , Priyanka Gupta (2020). Common Coupled Fixed Point Theorems for Weakly F-contractive Mappings in Topological Spaces. Mathematics and Statistics, 8(4), 382 - 387. DOI: 10.13189/ms.2020.080402.