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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Veröffentlicht in:	Mathematics (Basel) Jg. 13; H. 1; S. 163
Hauptverfasser:	Eljaneid, Nidal H. E., Alshaban, Esmail, Alatawi, Adel, Ali, Montaser Saudi, Alsharari, Saud S., Khan, Faizan Ahmad
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Basel MDPI AG 01.01.2025
Schlagworte:	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
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Abstract	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.
AbstractList	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.
Audience	Academic
Author	Alshaban, Esmail Khan, Faizan Ahmad Alsharari, Saud S. Ali, Montaser Saudi Alatawi, Adel Eljaneid, Nidal H. E.
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Cites_doi	10.1090/S0002-9939-03-07220-4 10.1007/978-981-10-4337-6_9 10.3390/axioms12050478 10.3934/math.2024305 10.1515/dema-2013-0388 10.1007/s11083-005-9018-5 10.18514/MMN.2022.3220 10.18514/MMN.2019.2468 10.1007/s42835-024-01933-5 10.1016/j.na.2009.01.240 10.3390/math11091976 10.1016/j.rinp.2023.107183 10.1016/j.chaos.2024.115440 10.2298/FIL1714421A 10.1007/s11071-024-09635-3 10.24193/fpt-ro.2018.1.02 10.1216/rmj.2024.54.161 10.1017/S0004972700001659 10.1007/s11784-012-0081-4 10.1016/S0362-546X(01)00388-1 10.3390/math12091275 10.3390/axioms11090441 10.1007/978-94-010-2715-1_5 10.1007/s11784-015-0247-y 10.1090/S0002-9939-1969-0239559-9
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SubjectTerms	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
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Title	Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems
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