Fixed Point Theorems for Nonexpansive Mappings under Binary Relations

Aftab Alam, Reny George, Mohammad Imdad and Md Hasanuzzaman
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Aftab Alam: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Reny George: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Mohammad Imdad: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Md Hasanuzzaman: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2021, vol. 9, issue 17, 1-10

Abstract: In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the R -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.

Keywords: binary relation; ?-nonexpansive maps; uniformly convex Banach space; ?-Krasnoselskii sequence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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