In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

Abstract In this paper we propose a solution to the nonlinear Fredholm integral equations in context of w -distance. For purpose, also provide fixed point result same setting. addition, best proximity results. We give examples and present numerical results approximate points.

In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal and Berinde-type weak obtain common best proximity points for these in setting F−metric spaces. Further, point result α−φ−proximal As an application, fixed coincidence results obtained. Some examples provided to support validity our main results....

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs maps to p-cyclic maps. find sufficient conditions existence and uniqueness points. illustrate results with an example that covers a wide class