Abstract
Samet
et al
. (Nonlinear Anal. 75:2154-2165, 2012) introduced
α
-
ψ
-contractive mappings and proved some fixed point results for these mappings. More recently Salimi
et al.
(Fixed Point Theory Appl. 2013:151, 2013) modified the notion of
α
-
ψ
-contractive mappings and established certain fixed point theorems. Here, we continue to utilize these modified notions for single-valued Geraghty and Meir-Keeler-type contractions, as well as multi-valued contractive mappings. Presented theorems provide main results of Hussain
et al
. (J. Inequal. Appl. 2013:114, 2013), Karapinar
et al
. (Fixed Point Theory Appl. 2013:34, 2013) and Asl
et al.
(Fixed Point Theory Appl. 2012:212, 2012) as corollaries. Moreover, some examples are given here to illustrate the usability of the obtained results.
MSC:
46N40, 47H10, 54H25, 46T99.