Fixed Point Theorems for Nonexpansive Mappings under Binary Relations

Fixed Point Theorems for Nonexpansive Mappings under Binary Relations

In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script...

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Bibliographic Details
Main Authors: Aftab Alam, Reny George, Mohammad Imdad, Md Hasanuzzaman
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
binary relation
ℛ-nonexpansive maps
uniformly convex Banach space
ℛ-Krasnoselskii sequence
Online Access:https://www.mdpi.com/2227-7390/9/17/2059
Description
Summary:In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>-Krasnoselskii sequence. We observe that graphical versions (Fixed Point Theory Appl. 2015:49 (2015) 6 pp.) and order-theoretic versions (Fixed Point Theory Appl. 2015:110 (2015) 7 pp.) of such results can be extended to a transitive binary relation.
ISSN:2227-7390

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