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


Girgin E., Buyukkaya A., Kuru N. K., ÖZTÜRK M.

AXIOMS, sa.7, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/axioms13070441
  • Dergi Adı: AXIOMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.