Reich–Krasnoselskii-type fixed point results with applications in integral equations

Abstract In this paper, motivated by Reich contraction and tool of measure of noncompactness, some generalizations of Reich, Kannan, Darbo, Sadovskii, and Krasnoselskii type fixed point results are presented by considering a pair of maps A, B on a nonempty closed subset M of a Banach space X into X....

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Bibliographic Details
Main Authors: Akbar Azam, Nayyar Mehmood, Niaz Ahmad, Faryad Ali
Format: Article
Language:English
Published: SpringerOpen 2023-10-01
Series:Journal of Inequalities and Applications
Subjects:
Online Access:https://doi.org/10.1186/s13660-023-03022-z
Description
Summary:Abstract In this paper, motivated by Reich contraction and tool of measure of noncompactness, some generalizations of Reich, Kannan, Darbo, Sadovskii, and Krasnoselskii type fixed point results are presented by considering a pair of maps A, B on a nonempty closed subset M of a Banach space X into X. The existence of a solution to the equation A x + B x = x $Ax+Bx=x$ , where A is k-set contractive and B is a generalized Reich contraction, is established. As applications, it is established that the main result of this paper can be applied to learn conditions under which a solution of a nonlinear integral equation exists. Further we explain this phenomenon with the help of a practical example to approximate such solutions by using fixed point techniques. The graphs of exact and approximate solutions are also given to attract readers for further research activities.
ISSN:1029-242X