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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantic...
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2025-01-01
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| author | Nidal H. E. Eljaneid Esmail Alshaban Adel Alatawi Montaser Saudi Ali Saud S. Alsharari Faizan Ahmad Khan |
| author_facet | Nidal H. E. Eljaneid Esmail Alshaban Adel Alatawi Montaser Saudi Ali Saud S. Alsharari Faizan Ahmad Khan |
| author_sort | Nidal H. E. Eljaneid |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif-italic">ϝ</mi></semantics></math></inline-formula>-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. |
| format | Article |
| id | doaj-art-d9e1ebb39af6498986be3ac1df213ca6 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d9e1ebb39af6498986be3ac1df213ca62025-01-10T13:18:28ZengMDPI AGMathematics2227-73902025-01-0113116310.3390/math13010163Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value ProblemsNidal H. E. Eljaneid0Esmail Alshaban1Adel Alatawi2Montaser Saudi Ali3Saud S. Alsharari4Faizan Ahmad Khan5Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Science Faculty, Northern Border University, Arar 73213, Saudi ArabiaDepartment of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi ArabiaThe intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif-italic">ϝ</mi></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/13/1/163fixed pointsbinary relationsgeneralized weak contractionsboundary value problems |
| spellingShingle | Nidal H. E. Eljaneid Esmail Alshaban Adel Alatawi Montaser Saudi Ali Saud S. Alsharari Faizan Ahmad Khan Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems Mathematics fixed points binary relations generalized weak contractions boundary value problems |
| title | Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems |
| title_full | Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems |
| title_fullStr | Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems |
| title_full_unstemmed | Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems |
| title_short | Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems |
| title_sort | generalized weak contractions involving a pair of auxiliary functions via locally transitive binary relations and applications to boundary value problems |
| topic | fixed points binary relations generalized weak contractions boundary value problems |
| url | https://www.mdpi.com/2227-7390/13/1/163 |
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