Fixed point results on θ-metric spaces via simulation functions

Abstract

In a recent article, Khojasteh et al. introduced a new class of simulation functions, Z-contractions, with blending over known contractive conditions in the literature. Subsequently, in this paper, we extend and generalize the results on θ-metric context and we discuss some fixed point results in connection with existing ones. Also, we originate the notion of modified Z−contractions and explore the existence and uniqueness of fixed points of such functions on the said spaces. Finally we include examples to instantiate our main results.

Contractive mapping theorems in Partially ordered metric spaces

“…Thereafter vigorous research work has been obtained by weakening its hypotheses on various spaces such as rectangular metric spaces, pseudo metric spaces, fuzzy metric spaces, quasi metric spaces, quasi semi-metric spaces, probabilistic metric spaces, D-metric spaces, G-metric spaces, F -metric spaces, cone metric spaces, and so on to prove the existing results. Prominent work on the existence and uniqueness of a fixed point and common fixed point theorems involving monotone mappings on cone metric spaces, partially ordered metric spaces and others spaces [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] generate natural interest to establish usable fixed point results.…”

Simulations functions and Geraghty type results

“…On the other hand, in 2015, Khojasteh et al [12] originated the notion of Zcontractions using a specific family of functions called simulation functions. Subsequently, many researchers generalized this idea in many ways ( [5,6,13,14,15,16,17,18,22] and references therein) and proved many interesting results in the arena of fixed point theory.…”

Influence of θ-metric spaces on the diameter of rough weighted I2-limit set

“…On the other hand, the idea of θ-metric space is a generalization of metric space, which was first defined by Khojasteh et al [20] in the year 2013 and most recently in 2017 related to the subject Chanda et al [5] proved some important results on fixed point theorem related to θ-metric space.…”