Abstract
The main outcome of this paper is to introduce the notion of orthogonal gauge spaces and to present some related fixed-point results. As an application of our results, we obtain existence theorems for integral equations.
Highlights
Fixed-point theory is a very important tool for proving the existence and uniqueness of the solutions to various mathematical models, such as integral and partial differential equations, optimization, variational inequalities, and approximation theory
Gordji et al [6] introduced an exciting notion of the orthogonal sets after which, orthogonal metric spaces were introduced. e concept of a sequence, continuity, and completeness has been redefined in this space
They gave an extension of the Banach fixed-point theorem on this newly described shape and applied their theorem to show the existence of a solution for a differential equation, which cannot be applied by the Banach fixed-point theorem
Summary
Fixed-point theory is a very important tool for proving the existence and uniqueness of the solutions to various mathematical models, such as integral and partial differential equations, optimization, variational inequalities, and approximation theory. E concept of a sequence, continuity, and completeness has been redefined in this space They gave an extension of the Banach fixed-point theorem on this newly described shape and applied their theorem to show the existence of a solution for a differential equation, which cannot be applied by the Banach fixed-point theorem. In 2013, Ali et al [18] ensured the existence of fixed points for an integral operator via a fixed-point theorem on complete gauge spaces. In 2012, Wardowski [19] gave a new type of contractions, named as F-contractions, and established new related fixed-point results. We apply the concept of orthogonality in gauge spaces and investigate the existence of solutions of integral equations through the fixed-point theorem on orthogonal complete gauge spaces
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