Certain New Development to the Orthogonal Binary Relations

Abstract

In this study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a generalization of the dynamic system (DS), which improves the existing results for analysies such as those presented here. By applying this, some new refinements of the F⊥-Suzuki-type (F⊥-ST) fixed-point results are presented. These include some tangible instances, and applications in the field of nonlinear analysis are given to highlight the usability and validity of the theoretical results.

Solving Differential Equation via Orthogonal Branciari Metric Spaces

“…Nazam et al [15] demonstrated the concept of ðΨ, ΦÞ-orthogonal interpolation contraction mappings. The notion of B metric-like space via a hybird pair of operators was introduced by Ali et al [16] in 2022. In 2021, Hussain [17] presented another family of fractional symmetric α-η-contractions and builds up some new results for such contraction in the context of F-metric space.…”

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

“…In the past few decades, many authors have extended and generalized the Banach contraction mapping principle in several ways (see [2][3][4][5][6][7][8][9][10][11][12]). On the other hand, several authors, such as Boyd and Wong [13], Browder [14], Wardowski [15], Jleli and Samet [16], and many other researchers have extended the Banach contraction principle by employing different types of control functions (see [17][18][19][20][21] and the references therein). Alam et al [22] introduced the concept of the relation-theoretic contraction principle and proved some well known fixed-point results in this area.…”