Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings


Authors

Monther Rashed Alfuraidan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. Sami Atif Shukri - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.


Abstract

In this paper, we prove the analog to Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings in complete hyperbolic metric spaces uniformly convex. In the linear case, this result is refined. Indeed, we prove that if X is a Banach space uniformly convex in every direction endowed with a graph \(G\), then every \(G\)-nonexpansive mapping \(T : A \rightarrow A\), where \(A\) is a nonempty weakly compact convex subset of \(X\), has a fixed point provided that there exists \(u_0 \in A\) such that \(T(u_0)\) and \(u_0\) are \(G\)-connected.


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ISRP Style

Monther Rashed Alfuraidan, Sami Atif Shukri, Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4078--4083

AMA Style

Alfuraidan Monther Rashed, Shukri Sami Atif, Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings. J. Nonlinear Sci. Appl. (2016); 9(6):4078--4083

Chicago/Turabian Style

Alfuraidan, Monther Rashed, Shukri, Sami Atif. "Browder and Göhde fixed point theorem for \(G\)-nonexpansive mappings." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4078--4083


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