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On modified α-Φ-asymmetric Meir-Keeler contractive mappings

Salimi P. (Islamic Azad University, Young Researchers and Elite Club, Rasht Branch, Rasht, Iran)
Hussain N. (Islamic Azad University, Department of Mathematic, Jeddah, Saudi Arabia)
Roldan A. (University of JaÉen, Campus las Lagunillas, JaÉen, Spain)
Karapınar E. (Atilim University, Department of Mathematics, Incek, Ankara, Turkey)

Samet et al. [Nonlinear Anal. 75:2154-2165, 2012] introduced and studied α-ψ-contractive mappings. More recently Salimi, et al. [Fixed Point Theory Appl., 2013:151] modified the notion of α-ψ-contractive mappings and improved the fixed point theorems in [20, 32]. Here we utilize these notions to establish fixed point results for modified α-Φ-asymmetric Meir-Keeler contractions and triangular α-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.

Keywords: α-ψ-contractions, α-Φ-asymmetric Meir-Keeler contractions, triangular α-admissible mappings, G-metric space