Abstract
In this article, for a tυs-G-cone metric space (X, G) and for the family of subsets of X, we introduce a new notion of the tυs - H - cone metric with respect to G, and we get a fixed result for the stronger Meir-Keeler-G-cone-type function in a complete tυs-G-cone metric space ( A , H ) Our result generalizes some recent results due to Dariusz Wardowski and Radonevic' et al.MSC: 47H10; 54C60; 54H25; 55M20.
Highlights
1 Introduction and preliminaries Recently, Huang and Zhang [1] introduced the concept of cone metric space by replacing the set of real numbers by an ordered Banach space, and they showed some fixed point theorems of contractive type mappings on cone metric spaces
Many authors like Abbas and Jungck [2] had generalized the results of Huang and Zhang [1] and studied the existence of common fixed points of a pair of self mappings satisfying a contractive type condition in the framework of normal cone metric spaces
In the articles [16,17,18,19], the authors tried to generalize this approach by using cones in topological vector spaces tυs instead of Banach spaces
Summary
Introduction and preliminariesRecently, Huang and Zhang [1] introduced the concept of cone metric space by replacing the set of real numbers by an ordered Banach space, and they showed some fixed point theorems of contractive type mappings on cone metric spaces. Many authors like Abbas and Jungck [2] had generalized the results of Huang and Zhang [1] and studied the existence of common fixed points of a pair of self mappings satisfying a contractive type condition in the framework of normal cone metric spaces.
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