Abstract
A generalization, namely the K-comparison function, of a comparison function is introduced. Using K-comparison functions we introduce $K_{G}$ -contractive mappings. We obtain a fixed point theorem for such mappings on partial Hausdorff metric spaces endowed with a graph. We also construct examples in support of our results.
Highlights
1 Introduction Development in metric fixed point theory is based on two things: the first is to modify contraction condition and the second is to modify the structure of a metric space
Jachymaski [ ] generalized the Banach fixed point theorem for mappings of a complete metric space endowed with a graph
We introduce the notions of a K -comparison function and a KG-contractive mapping
Summary
Development in metric fixed point theory is based on two things: the first is to modify contraction condition and the second is to modify the structure of a metric space. They [ ] extended Nadler’s fixed point theorem in the setting of a partial Hausdorff metric spaces.
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