in this paper, using the best proximity theorems for an extensionof brosowski's theorem. we obtain other results on farthest points. finally, wedene the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...

Let S : A→ B and T : A→ B be given non-self mappings, where A and B are non-empty subsets of a metric space. As S and T are non-self mappings, the equations Sx = x and T x = x do not necessarily have a common solution, called a common fixed point of the mappings S and T . Therefore, in such cases of nonexistence of a common solution, it is attempted to find an element x that is closest to both ...

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...

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....