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.
AMS Subject Classification:
47H10, 54H25.