COMMON FIXED POINT THEOREMS UNDER GENERALIZED (ψ-φ)-WEAK CONTRACTIONS IN S-METRIC SPACES WITH APPLICATIONS

Objective/Aim: To establish the existence and uniqueness of fixed points for self maps in b-metric spaces. Methods: We have used generalized 𝜑-weak contractive condition involving cubic terms of d(x, y) and weak compatibility of two maps in the setting of b-metric spaces. Findings: Some fixed point theorems for a self map and common fixed point theorems for two maps have been proved and some suitable examples are also given to justify the proven results. Novelty: In b-metric spaces, the existence of fixed points for mappings satisfying generalized 𝜑-weak contractive conditions involving cubic terms of d(x, y) has not been proved yet by others. Furthermore, our results extend and generalize the results of Dutta and Choudhury, Murthy and Prasad, Hao and Guan, Jain and Kaur, Petru, sel, A. and Petru, sel, J., Peng et. al. etc. Mathematics Subject Classification: 54H25, 47H10. Keywords: Fixed Point, b-Metric Space, φ –Weak Contraction, Generalized φ –Weak Contraction, Weakly Compatible Mapping

Weak condition for generalized multi-valued [formula omitted]-weak contraction mappings

Fixed point theorems had been established and developed under various non-expansive type conditions on different metric spaces. In this paper, we have generalized (ψ,φ) - weak contractions, which is the generalizations of F-contraction, (ϕ,F)-contraction as well as (ψ,φ)-contractions. Then we have established some unique common fixed point results for a sequence of mappings for (ψ,φ)- weak contractions in 2-Banach spaces. Some basic definitions, properties and examples are given in the introduction and preliminaries part. Some corollaries are also given on the basis on the results.

The Banach contraction principle is the most important result. This principle has many applications and some authors was interested in this principle in various metric spaces as Brianciari.
 The author initiated the notion of the generalized metric space as a generalization of a metric space by replacing the triangle inequality by a more general inequality, $d(x,y)\leq d(x,u)+d(u,v)+d(v,y)$ for all pairwise distinct points $x,y,u,v$ of $X$. As such, any metric space is a generalized metric space but the converse is not true. He proved the Banach fixed point theorem in such a space. Some authors proved different types of fixed point theorems by extending the Banach's result. Wardowski introduced a new contraction, which generalizes the Banach contraction. He using a mapping $F: \mathbb{R}^{+} \rightarrow \mathbb{R}$ introduced a new type of contraction called $F$-contraction and proved a new fixed point theorem concerning $F$-contraction. In this paper, we have dealt with $F$-contraction and $F$-weak contraction in complete generalized metric spaces. We prove some results for $F$-contraction and $F$-weak contraction and we show that the existence and uniqueness of fixed point for satisfying $F$-contraction and $F$-weak contraction in complete generalized metric spaces. Some examples are supplied in order to support the useability of our results. The obtained result is an extension and a generalization of many existing results in the literature.

Multivalued [formula omitted]-weakly Picard mappings

The aim of this paper is to prove some important fixed-point theorems in the context of the neutrosophic metric space, which is a generalization of the fuzzy Banach fixed-point theorem, by utilizing the control function. Also, certain fixed-point theorems in the G-complete neutrosophic metric space are proved and discussed by utilizing the alternating distance function (ADF) and defined neutrosophic -weak contraction. The current study supports the results with some non-trivial examples. Furthermore, it also supports the main result with an application of the Fredholm integral equation.

Weak contraction mapping principle is a generalization of the Banach contraction mapping principle. Weakly contractive mappings are intermediate to contraction mappings and nonexpansive mappings. They have been studied in several contexts. Metric fixed point theory in partially ordered spaces have rapidly developed in recent times. In this paper we extend the concept of weak contraction to subset of a partially ordered generalized metric space which are chains by themselves. It is noted that this weak contraction is different from weak contraction on the whole space. We prove here that under certain assumptions the weakly contractive mapping on certain chains will have a fixed point. Two illustrative examples are given.

The aim of this paper is to establish some new common fixed point theorems for mappings employing -weak contraction in fuzzy metric spaces. Our results generalize and improve various well known comparable results

The fixed point theory is the most important topic in mathematics anaysis. This topic has many applications in the different fields. It demonstrates the uniqueness of the existence of a mapping and how it can be found. The Banach contraction mapping principle is most important theorem in the fixed point theory. Most authors have introduced new contractions and they proved some fixed point theorems in metric spaces. On the other hand, some authors introduced new metric spaces as a generalization of metric spaces. Later, they proved fixed point theorems which generalize the Banach contraction principle for various mappings in several metric spaces. The purpose of this study is to introduce the existence and uniqueness of ϕ-fixed point for some new contractions in complete b-metric spaces. Firstly, we presented new definitions called (F,ϕ,α,θ)_{s} and (F,ϕ,α,θ)_{s}-weak contractions in complete b-metric spaces as a generalization of metric spaces. Later, we proved ϕ-fixed point theorems for (F,ϕ,α,θ)_{s} and (F,ϕ,α,θ)_{s}-weak contractions in complete b-metric spaces. The presented theorems extend and generalize some ϕ-fixed point results which are known in the literature. As applications, we derived some fixed point results in complete partial b-metric spaces as a generalization of partial metric spaces. The results in this paper generalizes may existing results in the literature.

In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and - (,)-Weak contraction mappings in Banach spaces.

In this paper, we introduce weakly generalized (ψ, φ)-weak quasi contraction for four self-maps and establish a common fixed point theorem using weak compatible property.

The aim of this paper is to establish some fixed point and common fixed point theorems for (psi -phi )-almost weak contractions in complete S-metric spaces, followed by some supportive examples. Our results extend and generalize several results existing in the literature. We employ the outcomes of the fixed point theorems to establish the existence and uniqueness of a solution for a class of conformable differential equations which is a new branch of fractional calculus.

In this paper, we prove some common fixed point theorems in 0-complete partial metric spaces. Our results extend and generalize many existing results in the literature. Some examples are included which show that the generalization is proper.