On the Existence of Solutions to a Boundary Value Problem via New Weakly Contractive Operator

In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is obs...

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Bibliographic Details
Published in:Axioms 2023-04, Vol.12 (4), p.397
Main Authors: Chiroma, Rhoda, Alotaibi, Trad, Shehu Shagari, Mohammed, Bakery, Awad A., Mohammed, OM Kalthum S. K., Mustafa, Arafa O.
Format: Article
Language:English
Subjects:
Boundary value problems
Differential equations
fixed point
Investigations
Mathematical research
metric-like spaces
Operator theory
partial metric spaces
weakly contractive
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Summary:In this paper, the notion of generalized quasi-weakly contractive operators in metric-like spaces is introduced, and new conditions for the existence of fixed points for such mappings are investigated. A non-trivial example which highlights the novelty of our principal idea is constructed. It is observed comparatively that the proposed concepts herein subsume some important results in the corresponding literature. As an application, one of our obtained findings is utilized to setup novel criteria for the existence of solutions to two-point boundary value problems of a second order differential equation. To attract new researchers in the directions examined in this article, a significant number of corollaries are pointed out and discussed.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12040397