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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Vydáno v:	Mathematics (Basel) Ročník 13; číslo 1; s. 163
Hlavní autoři:	Eljaneid, Nidal H. E., Alshaban, Esmail, Alatawi, Adel, Ali, Montaser Saudi, Alsharari, Saud S., Khan, Faizan Ahmad
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel MDPI AG 01.01.2025
Témata:	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
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math13010163