Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems

The intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions ϕ and ψ verifying appropriate properties. In proving our outcomes, we observed that the partial-ordered relation (even, transi...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 13; no. 1; p. 163
Main Authors: Eljaneid, Nidal H. E., Alshaban, Esmail, Alatawi, Adel, Ali, Montaser Saudi, Alsharari, Saud S., Khan, Faizan Ahmad
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2025
Subjects:
Analysis
binary relations
Boundary value problems
Contraction operators
Distributions, Theory of (Functional analysis)
Fixed point theory
fixed points
generalized weak contractions
Tests, problems and exercises
Saudi Arabia
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:The intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions ϕ and ψ verifying appropriate properties. In proving our outcomes, we observed that the partial-ordered relation (even, transitive relation) adopted by earlier authors can be weakened to the extent of a locally ϝ-transitive binary relation. The findings proved herewith generalize, extend, improve, and unify a number of existing outcomes. To validate of our findings, we offer a number of illustrative examples. Our outcomes assist us to figure out the existence and uniqueness of solutions to a boundary value problem.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math13010163