Khursheed J. Ansari

Aug 4, 2023 | mdpi.com | Khursheed J. Ansari |Salvatore Sessa |Aftab Alam

Abstract:In this article, we investigate some fixed-point results under certain functional contractive mappings in a relation metric space. In the process, we utilize more general contraction condition which must be verified for comparative elements only. Our results enrich, modify, refine, unify and sharpen several existing fixed-point results. We construct some examples in support of our results.

May 29, 2023 | mdpi.com | Arshad Ali |Hussam Alrabaiah |Ahmad Aloqaily |Khursheed J. Ansari

Abstract:In this research paper, we study a coupled system of piecewise-order differential equations (DEs) with variable kernel and impulsive conditions. DEs with variable kernel have high flexibility due to the freedom of changing the kernel. We study existence and stability theory and derive sufficient conditions for main results of the proposed problem. We apply Scheafer’s fixed point theorem and Banach fixed point theorem for the result of at least one and unique solution, respectively.