Meir-Keeler α-contractive fixed and common fixed point theorems

Abstract

Generalized Meir-Keeler α-contractive functions and pairs are introduced and their fixed and common fixed point theorems are obtained. Also, the so-called generalized Meir-Keeler α-f-contractive maps commuting with f are introduced and their coincidence and common fixed point theorems are investigated. New sufficient conditions different from those in (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012) are used. An application to the coupled fixed point is established as well. An example is given to show that the α-Meir-Keeler generalization is real. © 2013 Abdeljawad; licensee Springer.