On modified $\alpha$-$\phi$-asymmetric Meir-Keeler contractive mappings

Abstract

Samet et al. [Nonlinear Anal. 75:2154-2165, 2012] introduced and
studied $\alpha$-$\psi$-contractive mappings. More recently Salimi,
et al. [Fixed Point Theory Appl., 2013:151] modified the notion of
$\alpha$-$\psi$-contractive mappings and improved the fixed point
theorems in [19, 32] Here we  utilize these notions to
establish fixed point results for modified
$\alpha$-$\phi$-asymmetric Meir-Keeler contractions and triangular
$\alpha$-admissible mappings defined on G-metric and cone G-metric
spaces. Several interesting consequences of our theorems are also
provided here to illustrate the usability of the obtained results.