On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in <inline-formula><math display="inline"><semantics><mi mathvariant="bold-fraktur">R</mi></semantics></math></inline-formula>-Modular <i>b</i>-Metric-like Spaces

Abstract

In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both 𝒵 simulation function and E-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation R. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit.

Keywords

• fixed point
• simulation functions
• modular metric-like space
• dynamic programming
• electric circuit equation