Abstract
This paper proves a common fixed point theorem for single-valued and multivalued mappings by using ternary relation in G -metric spaces. Henceforth, results obtained will be verified with the help of illustrative examples. Also, we demonstrate the results with an application.
Highlights
In 1969, Nadler [1] introduced multivalued contraction mappings using the Hausdorff metric and extended Banach’s contraction principle [2] from single-valued to multivalued mappings
This paper proves a common fixed point theorem for single-valued and multivalued mappings by using ternary relation in G -metric spaces
Several researchers have generalized these results for multivalued mappings in various spaces
Summary
In 1969, Nadler [1] introduced multivalued contraction mappings using the Hausdorff metric and extended Banach’s contraction principle [2] from single-valued to multivalued mappings. Kaneko and Sessa [3] extended the concept of compatible mappings due to Jungck [4] to include multivalued mappings as well as single-valued mappings They followed the works of Kubiak [5] and Nadler [1] and proved coincidence and fixed point theorems for hybrid pair of compatible mappings. Tahat et al [11] proved common fixed points for single-valued and multivalued maps satisfying a generalized contraction in G-metric spaces. Gaba et al [23] extended the works of Alam and Imdad [14] by using the Banach contraction mapping principle in generalized metric spaces with a ternary relation. This paper is aimed at proving a common fixed point theorem for single-valued and multivalued mappings by using the ternary relation concept in the G-metric space setting. We will generalize several other works in the literature having the same directions
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