A fixed point theorem on soft G-metric spaces

Abstract

We introduce soft G-metric spaces via soft element. Then, we obtain soft convergence and soft continuity by using soft G-metric. Also, we prove a fixed point theorem for mappings satisfying sufficient conditions in soft G-metric spaces.

Remarks on fixed point theory in soft metric type spaces

“…We begin this section by recalling some definitions and fixed point results in soft G-metric spaces in [10]. Throughout this section, we will use E as a set of parameters.…”

“…Definition 3.5. [10] Let (X,G, E) be a soft G-metric space. Let T : (X,G, E) → (X,G, E) be a mapping.…”

Common Fixed Point Theorems via Implicit Contractions in Soft Quasi Metric Spaces

“…Definition 1.4. ( [3]) Let X be a nonempty set and E be the nonempty set of parameters. A mapping G : SE( X) × SE( X) × SE( X) → R(E) * is said to be a soft generalized metric or soft G-metric on X, if G satisfies the following conditions:…”

“…Proposition 1.8. ( [3]) Let ( X, G, E) be a soft G-metric space, for a sequence ( x n ) in X and soft element x, then the followings are equivalent:…”

Some soft topological properties and fixed soft element results in soft complex valued metric spaces

“…Abbas et al [2] established soft metric versions of several important fixed point theorems for metric spaces. Then, Guler et al [11] introduced soft G-metric spaces with the help of soft elements and proved fixed point theorems on these spaces.…”