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

• Published in: Axioms Vol. 12; no. 4; p. 397
• Main Authors: Chiroma, Rhoda, Alotaibi, Trad, Shehu Shagari, Mohammed, Bakery, Awad A., Mohammed, OM Kalthum S. K., Mustafa, Arafa O.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-04-2023
• Subjects: Boundary value problems; Differential equations; fixed point; Investigations; Mathematical research; metric-like spaces; Operator theory; partial metric spaces; weakly contractive; Nigeria
• ISSN: 2075-1680; 2075-1680
• DOI: 10.3390/axioms12040397

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.