Fixed point theorems under conditional semicompatibility with control function

Abstract

The aim of the present paper is to generalize the elegant work of Pathak et al.[17] by using the new notion of “conditional semicompatibility”. The new notion is proper generalization of semi compatibility and weak semi compatibility and can be applicable on commuting and compatible maps. We used compatible mappings, commuting mappings and absorbing mappings to prove theorems which also include (E.A.) property. In the last section we show that the new notion is a necessary condition for the existence of common fixed points.