Nonlinear Contractive Condition Research Articles

Certain Fixed-Point Results via DS-Weak Commutativity Condition in Neutrosophic Metric Spaces With Application to Non-linear Fractional Differential Equations

This study demonstrates that, for the non-linear contractive conditions in Neutrosophic metric spaces, a common fixed-point theorem may be proved without requiring the continuity of any mappings. A novel commutativity requirement for mappings weaker than the compatibility of mappings is used to demonstrate the conclusion. We provide several examples to illustrate our major idea. Also, we provide an application to the non-linear fractional differential equation to show the validity of our main result.

Common fixed-point theorems for non-linear non-self contractive mappings in convex metric spaces

Abstract In this article, two pairs of non-self mappings satisfying a collection of non-linear contractive conditions in convex metric space are considered to prove a common fixed-point theorem. An appropriate example is provided to support the results proved herein. In addition, we have proved a theorem as an application of our main result. Our results generalize and extend several existing theorems in the literature.

Some fixed point results for nonlinear contractive conditions in ordered proximity spaces with an application

<abstract><p>In this article, we use the concept of proximity spaces to prove common fixed point results for mappings satisfying generalized ($ \psi $, $ \beta $)-Geraghty contraction type mapping in partially ordered proximity spaces. Finally, we investigate an application to endorse our results.</p></abstract>

Orbital Continuity and Common Fixed Points in Menger PM-Spaces

In this paper, we prove that if a pair of semi R-commuting self-mappings defined on Menger PM-spaces with a nonlinear contractive condition posses a unique common fixed point, then these mappings are orbitally continuous. Also, we investigate whether this assertion and it converse holds if we replace semi R-commutativity with some other concept of commutativity in the weaker sense.

Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results.

Some Fixed Point Results in Partial Rectangular Metric-Like Spaces

In this paper, we introduce a new concept of partial rectangular metric-like space and prove some results on the existence and uniqueness of a fixed point of a functionT:X⟶X, defined on a partial rectangular metric-like spaceX, which fulfills a nonlinear contractive condition using a comparison function and the diameter of the orbits. The obtained results generalize some previously acknowledged results in partial metric spaces, partial rectangular metric spaces, and rectangular metric-like spaces. The examples presented prove the usefulness of the introduced generalizations.

A characterisation of completeness of b-fuzzy metric spaces and nonlinear contractions

The purpose of this paper is to present a common fixed point theorem for a pair of R-weakly commuting mappings defined on b-fuzzy metric spaces satisfying nonlinear contractive conditions of Boyd-Wong type, obtained in D. W. Boyd, J. S. W. Wong: On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.

Fixed Point Theorems For Non-Self Mappings With Nonlinear Contractive Condition In Strictly Convex Menger $$PM\mbox{-}$$Spaces

We prove existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition defined in strictly convex Menger $$PM\mbox{-}$$ spaces.

Fixed point Theorems for Non-self mappings with nonlinear contractive condition in strictly convex FCM-spaces

In this paper we define convex, strict convex and normal structures for sets in fuzzy cone metric spaces. Also, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition will be proved, using the notion of strictly convex structure. Moreover, we give some examples illustrate our results.

Random Common Fixed Point Theorems for Two Pairs of Nonlinear Contractive Maps in Polish Spaces

This research work proves the random common fixed point theorem for two pairs of random weakly compatible mappings fulfilling certain generalized random nonlinear contractive conditions in Polish spaces. An example is given to support the validity of our results. Our results generalize and extend some works in literature.

A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations

In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed.

Fixed Point Results for Mapping of Nonlinear Contractive Conditions of $\alpha$ -Admissibility Form

We introduce in this paper some concepts of α-admissible triangular mappings with respect to a function β and the concept of (α, β, ψ)-contraction. We also utilize our new concept to prove a fixed point theorem based on the contractive condition of type α-admissibility. We apply our main result to derive many fixed point results. Also, we construct some examples to support our work. In the literature, many exciting results are improved and extended using our results.

Common fixed point theorems for self-mappings in Menger PM-spaces with nonlinear contractive condition

The purpose of this paper is to prove some common fixed point theorems for a pair of self-mappings defined on Menger PM-spaces with nonlinear contractive condition in the sense of Fang (Fuzzy Set Syst 267:86–99, 2015). Following Pant and Pant (Filomat (31)(11):3495–3499, 2017), we define semi R-commutativity for a pair of self-mappings for Menger PM-spaces. Using this notion and the notion of orbital continuity introduced by Ciric (Publ Inst Math (12)(26):19–26, 1971), we obtain the main results. These results generalize some known results. Some examples and comments according to the preceding results are given.

Common fixed point results via implicit contractions for multi-valued mappings on b-metric like spaces

In this paper, motivated by the recent work [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537] some generalized nonlinear contractive conditions via implicit functions and α-admissible pairs of multi-valued mappings in the setting of b-metric like spaces have been introduced. Some common fixed point results for such mappings in this framework have been provided. Then, some corollaries and consequences for our obtained results are given. Our results are the multi-valued versions of [Journal of Nonlinear Sciences and Applications, 10(4):1544–1537]. An example also is provided to support our obtained results. The presented results generalize and extend some earlier results in the literature.

Common fixed point results for $$\alpha $$ α -admissible mappings via simulation function

In 2015, Khojasteh et al. (Filomat 29(6):1189–1194, 2015) introduced the class of simulation functions and utilized the same to unify several fixed point results of the existing literature. Very recently, Karapinar (Filomat 30(8):2343–2350, 2016) enlarged this class to cover $$\alpha $$ -admissible contractions. Motivated by aforementioned articles, we establish common fixed point results for $$\alpha $$ -admissible mappings satisfying a nonlinear contraction condition under simulation function.

Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces

Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces

Altering distances and a common fixed point theorem in Menger probabilistic metric spaces

This paper presents a common fixed point theorem for two compatible self-mappings satisfying nonlinear contractive type condition defined using a ?-function. This result extends previous results due to B. S. Choudhury, K. Das, A new contraction principle in Menger spaces, Acta Mathematica Sinica 24 (2008) 1379-1386, and the result due to D. Mihe?, Altering distances in probabilistic Menger spaces, Nonlinear Analysis 71 (2009) 2734-2738.

Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

Common fixed point theorems for six self-maps in b -metric spaces with nonlinear contractive conditions

Common fixed point theorems for six self-maps in b -metric spaces with nonlinear contractive conditions

Probabilistic Generalized Metric Spaces and Nonlinear Contractions

Abstract We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.