Modified Suzuki-Simulation Type Contractive Mapping in Non-Archimedean Quasi Modular Metric Spaces and Application to Graph Theory

Ekber Girgin,Mahpeyker Öztürk

doi:10.3390/math7090769

Abstract

In this paper, we establish generalized Suzuki-simulation-type contractive mapping and prove fixed point theorems on non-Archimedean quasi modular metric spaces. As an application, we acquire graphic-type results.

Highlights

In the sequel, the letter R+ will denote the set of all nonnegative real numbers.Let S be a nonempty set and V : S → S be given mappings
Bindu et al [11] proved the commonfixed point theorem for Suzuki type mapping in a complete subspace of the partial metric space
Q is regular and convex and TZ denotes the family of all CG -simulation functions ζ : [0, ∞)2 → R

Summary

Introduction

The letter R+ will denote the set of all nonnegative real numbers. Let S be a nonempty set and V : S → S be given mappings. The mapping ζ is named a simulation function satisfying the following conditions:. A CG -simulation function is a mapping ζ : [0, ∞)2 → R satisfying the following conditions:. Bindu et al [11] proved the commonfixed point theorem for Suzuki type mapping in a complete subspace of the partial metric space. Jleli and Samet [12] introduced a Σ-contraction and established fixed point results in generalized metric spaces. Let (S, d) be a complete generalized metric space and V : S → S be a mapping. The class of functions Θwas defined by the set of Σ : (0, ∞) → (1, ∞) satisfying the following conditions: Σ1. We will establish a generalized Suzuki-simulation-type contractive mapping and obtain fixed point results

Quasi Modular Metric Space

Common Fixed Point Results

Application to a Graph Structure

Conclusions