On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces

Author:

Girgin Ekber1ORCID,Büyükkaya Abdurrahman2ORCID,Kuru Neslihan Kaplan3ORCID,Öztürk Mahpeyker3ORCID

Affiliation:

1. Department of Engineering Fundamental Sciences, Sakarya University of Applied Sciences, 54187 Serdivan, Sakarya, Türkiye

2. Department of Mathematics, Karadeniz Technical University, 61080 Ortahisar, Trabzon, Türkiye

3. Department of Mathematics, Sakarya University, 54187 Serdivan, Sakarya, Türkiye

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.

Publisher

MDPI AG

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