Existence of best proximity points for the sum of two operators

Abstract

In this paper, we work on the existence of approximate solution for the fixed point equation
Rx + Qx = x, when R is a weak contractive mapping and Q is a continuous self-map which is a new topic
related to the background literature. Till now, no results were found to find the existence of approximate
solution for such a kind of mappings in literature to the best of our knowledge. Here we prove the existence
of best proximity point for the sum of a weak contractive non self map and a continuous self map. Also,
we provide an example to support our main theorem. And also, we prove the existence of best proximity
point for the sum of Geraghty- contraction and continuous map.