Abstract
In this paper, we introduce the concept of Hausdorff G-metric in the space of fuzzy sets induced by the metric and obtain some results on Hausdorff G-metric. We also prove common fixed point theorems for a family of fuzzy self-mappings in the space of fuzzy sets on a complete G-metric space. MSC:47H10, 54H25.
Highlights
Introduction and preliminariesFixed point theory is very important in mathematics and has applications in many fields
We establish common fixed point theorems for a family of fuzzy self-mappings in the space of fuzzy sets on a complete G-metric space
4 Conclusion In this work, by using the new concept of Hausdorff G-metric in the space of fuzzy sets, we establish some common fixed point theorems for a family of fuzzy self-mappings in the space of fuzzy sets on a complete G-metric space
Summary
Fixed point theory is very important in mathematics and has applications in many fields. A number of authors established fixed point theorems for various mappings in different metric spaces. In , Mustafa and Sims [ ] introduced the G-metric space as a generalization of metric spaces. We recall some definitions and results in G-metric spaces in [ ]. Let X be a nonempty set, and let G : X × X × X → R+ be a function satisfying:
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