In this paper, first we introduce the notion of a $G^m$-Meir-Keeler contractive mapping and establish some fixed point theorems for the $G^m$-Meir-Keeler contractive mapping in the setting of $G$-metric spaces. Further, we introduce the notion of a $G_c^m$-Meir-Keeler contractive mapping in the setting of $G$-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a $G$-$(\alpha,\psi)$-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of $G$-metric spaces.
Hussain, N., Karapinar, E., Salimi, P., Vetro, P. (2013). Fixed point results for $G^m$-Meir-Keeler contractive and $G$-$(\alpha,\psi)$-Meir-Keeler contractive mappings. FIXED POINT THEORY AND APPLICATIONS, 2013, 1-14 [10.1186/1687-1812-2013-34].
Fixed point results for $G^m$-Meir-Keeler contractive and $G$-$(\alpha,\psi)$-Meir-Keeler contractive mappings
VETRO, Pasquale
2013-01-01
Abstract
In this paper, first we introduce the notion of a $G^m$-Meir-Keeler contractive mapping and establish some fixed point theorems for the $G^m$-Meir-Keeler contractive mapping in the setting of $G$-metric spaces. Further, we introduce the notion of a $G_c^m$-Meir-Keeler contractive mapping in the setting of $G$-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a $G$-$(\alpha,\psi)$-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of $G$-metric spaces.
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