0000000001018432
AUTHOR
E Karapinar
Fixed point results for $G^m$-Meir-Keeler contractive and $G$-$(\alpha,\psi)$-Meir-Keeler contractive mappings
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.
Optimization Problems via Best Proximity Point Analysis
Many problems arising in different areas of mathematics, such as optimization, variational analysis, and differential equations, can be modeled as equations of the form Tx=x, where T is a given mapping in the framework of a metric space. However, such equation does not necessarily possess a solution if T happens to be nonself-mapping. In such situations, one speculates to determine an approximate solution x (called a best proximity point) that is optimal in the sense that the distance between x and Tx is minimum. The aim of best proximity point analysis is to provide sufficient conditions that assure the existence and uniqueness of a best proximity point. This special issue is focused on th…