On α-ψ-Contractive Condition for Single-Valued and Multi-Valued Operators in Strong b-Metric Spaces

This paper aims to establish fixed point theorems in a complete strong b-metric space under the α-ψ-contractive condition imposed on single-valued mappings. Subsequently, we prove certain fixed point theorems, both locally and globally, under the α∗-ψ-contractive condition and the α-ψ-contractive condition on multi-valued mappings in a complete strong b-metric space. The theorems presented in this paper extend, generalize, and improve various existing results in the literature. To demonstrate the superiority of the results, we present multiple examples throughout this article and two applications: one in dynamic programming and another in ordinary differential equations. Moreover, the proposed results provide stronger and more general conclusions compared to several well-known fixed point theorems in the literature. In particular, our findings highlight the novelty and superiority of the α-ψ-contractive framework in the setting of strong b-metric spaces, offering broader applicability and deeper insight into both theoretical and applied contexts.