Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems
Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-uni...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/14/2226 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849303486118756352 |
|---|---|
| author | Doaa Filali Faizan Ahmad Khan |
| author_facet | Doaa Filali Faizan Ahmad Khan |
| author_sort | Doaa Filali |
| collection | DOAJ |
| description | Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, Boyd–Wong contraction, Pant contraction and relational contraction. We also establish the corresponding uniqueness theorem for the proposed contraction under some additional hypotheses. Several examples are furnished to illustrate the legitimacy of our newly proved results. In particular, we deduce a fixed-point theorem for almost Boyd–Wong contractions in the setting of abstract metric space. Our results generalize, enhance, expand, consolidate and develop a number of known results existing in the literature. The practical relevance of the theoretical findings is demonstrated by applying to study the existence and uniqueness of solution of a specific periodic boundary value problem. |
| format | Article |
| id | doaj-art-52fa136677b84c94aade4c2cc228a326 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-52fa136677b84c94aade4c2cc228a3262025-08-20T03:58:26ZengMDPI AGMathematics2227-73902025-07-011314222610.3390/math13142226Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value ProblemsDoaa Filali0Faizan Ahmad Khan1Department of Mathematical Science, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 84428, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi ArabiaNon-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, Boyd–Wong contraction, Pant contraction and relational contraction. We also establish the corresponding uniqueness theorem for the proposed contraction under some additional hypotheses. Several examples are furnished to illustrate the legitimacy of our newly proved results. In particular, we deduce a fixed-point theorem for almost Boyd–Wong contractions in the setting of abstract metric space. Our results generalize, enhance, expand, consolidate and develop a number of known results existing in the literature. The practical relevance of the theoretical findings is demonstrated by applying to study the existence and uniqueness of solution of a specific periodic boundary value problem.https://www.mdpi.com/2227-7390/13/14/2226fixed pointbinary relationcontrol functions |
| spellingShingle | Doaa Filali Faizan Ahmad Khan Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems Mathematics fixed point binary relation control functions |
| title | Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems |
| title_full | Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems |
| title_fullStr | Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems |
| title_full_unstemmed | Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems |
| title_short | Relation-Theoretic Boyd–Wong Contractions of Pant Type with an Application to Boundary Value Problems |
| title_sort | relation theoretic boyd wong contractions of pant type with an application to boundary value problems |
| topic | fixed point binary relation control functions |
| url | https://www.mdpi.com/2227-7390/13/14/2226 |
| work_keys_str_mv | AT doaafilali relationtheoreticboydwongcontractionsofpanttypewithanapplicationtoboundaryvalueproblems AT faizanahmadkhan relationtheoreticboydwongcontractionsofpanttypewithanapplicationtoboundaryvalueproblems |