On Modified $\alpha$-$\phi$-Asymmetric Meir--Keeler Contractive Mappings

P. Salimi, N. Hussain, A. Roldan, E. Karapınar

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 [20, 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.