Solving an Integral Equation via Orthogonal Branciari Metric Spaces

Abstract

In this article, we present an orthogonal L -contraction mapping concepts and prove a fixed point theorem on orthogonal complete Branciari metric spaces. As an application, we apply our major results to solving integral equations.

Common Fixed Point Theorems on Orthogonal Branciari Metric Spaces with an Application

“…In 2022, Aiman et al [42] defined the orthogonal Branciari (Rectangular) metric spaces as follows: Definition 12 ([42]). The triplet ( , ⊥, δ) is said to be an orthogonal Rectangular metric space if ( , ⊥) is an orthogonal set and ( , δ) is a Rectangular metric space.…”

“…The fixed point results in generalized orthogonal metric space and various metric spaces were proven by many researchers, see [35][36][37][38][39][40][41]. More recently, in 2022, Aiman et al [42] initiated an orthogonal Branciari metric space and proved the fixed point results thereon.…”

Solving Differential Equation via Orthogonal Branciari Metric Spaces

“…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. Mukheimer et al [18] initiated the concept of orthogonal L-contraction mapping and proved fixed-point results in OBMS.…”

Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces

“…And also, Eshaghi Gordji and Habibi [22] has extended and proved some fixed point theorem in generalized O-metric spaces. For other results related to orthogonal concepts, see [23][24][25][26][27][28][29][30].…”