Fixed-Circle Problem on S-Metric Spaces with a Geometric Viewpoint

Recently, a new geometric approach which is called the fixed-circle problem has been gained to fixed-point theory. The problem is introduced and studied using different techniques on metric spaces. In this paper, we consider the fixed-circle problem on $S$-metric spaces. We investigate existence and uniqueness conditions for fixed circles of self-mappings on an $S$-metric space. Some examples of self-mappings having fixed circles are also given.Comment: 15 pages, 2 figure

Korovkin type approximation theorems in weighted spaces via power series method

In this paper we consider power series method which is also member of the class of all continuous summability methods. We study a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space Cρ1 into a weighted space Bρ2 with the use of the power series method which includes both Abel and Borel methods. We also consider the rates of convergence of these operators. © 2018, Element D.O.O.. All rights reserved