Some new generalizations of Karapinar's theorems

Abstract

In-depth study of fixed point theory is to solve the existence of the equation Tx = x (or x ∈ T (x)), where T is a self-map or a non-self-map. However, as we know, the equation Tx = x (or x ∈ T (x)) is not necessarily to have a solution. So, we turn to explore the best approximation of the existence of solutions. In 2003, Kirk-Srinavasan-Veeramani [1] introduced cyclic maps and best proximity points. Many new results on cyclic maps have been obtained in the literature, see e.g. [2-11].