Points Of Mappings Research Articles

Some Common Fixed Point Theorems in Bipolar Metric Spaces

In this article, we introduce the notion of commutativity for covariant and contravariant mappings in bipolar metric spaces. Afterwards, by using this notion, we prove some common fixed point theorems which show the existence and uniqueness of common fixed point for covariant and contravariant mappings satisfying contractive type conditions.

Fixed point theorems for suzuki nonexpansive mappings in banach spaces

In this paper, we investigate the existence of fixed points for Suzuki nonexpansive mappings in the setting of Banach spaces using the asymptotic center technique. We also establish the convergence of regular approximate fixed point sequence to the fixed points of Suzuki nonexpansive mappings. Examples are also given to illustrate the results. Our theorems generalize several results in the literature.

A unique common fixed point for contractive mappings under a new concept

In this paper, we will investigate the existence and uniqueness of common fixed points of certain mappings in the frame of a metric space. The given results cover a number of unique common fixed point theorems especially a result of Phaneendra and Swatmaram [12]. We will also display two examples to illustrate our theorems.

INTEGRAL TYPE GENERALIZED CONTRACTION MAPPINGS IN MODULAR SPACES

In this paper we study the existence of common fixed point for r-compatible mapping satisfying a generalized quasi contraction condition of integral type in modular spaces Our results extend and generalize the results of Beygmohammadi and Razani [4] and Razani and Moradi [25].

Common fixed, coupled coincidence and common coupled fixed point results in hyperbolic valued metric spaces

In this paper, we obtain existence of unique common fixed point for a contraction mapping on hyperbolic valued metric spaces, and also develop some coupled coincidence point and common coupled fixed point results for two mappings satisfying various contractive conditions in such spaces. We also give some illustrative examples to validate our results.

On approximating fixed points of weak enriched contraction mappings via Kirk's iterative algorithm in Banach spaces

Recently Berinde and Păcurar [Approximating fixed points of enriched contractions in Banach spaces. {\em J. Fixed Point Theory Appl.} {\bf 22} (2020), no. 2., 1--10], first introduced the idea of enriched contraction mappings and proved the existence of a fixed point of an enriched contraction mapping using the well-known fact that any fixed point of {the averaged mapping $T_\lambda$, where $\lambda\in (0,1]$, is also a fixed point of the initial mapping $T$}. In this work, we introduce the idea of weak enriched contraction mappings, and a new generalization of an averaged mapping called double averaged mapping. The first attempt is to prove the existence and uniqueness of the fixed point of a double averaged mapping associated with a weak enriched contraction mapping. Based on this result on Banach spaces, we give some sufficient conditions for the equality of all fixed points of a double averaged mapping and the set {of all fixed points of a weak enriched contraction mapping.} Moreover, our results show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a weak enriched contraction mapping. An illustrative example for showing the efficiency of our results is given.

A generalized common fixed point of multi-valued maps in b-metric space

In this work we are interested to prove a general fixed point theorem for a pair of multi-valued mappings in b-metric spaces. The results in this paper generalize the results obtained in [19] and to obtain other particular results.

Existence, Data Dependence and Stability of Fixed Points of Multivalued Maps in Incomplete Metric Spaces

Abstract In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example.

Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of solutions of parameterized generalized equations, implicit function and fixed-point theorems, optimal value functions in parametric optimization, etc. Using the advanced machinery of variational analysis and generalized differentiation that furnishes complete characterizations of well-posedness properties of multifunctions, we establish a general theorem ensuring the existence of parameter-dependent coincidence point mappings with explicit error bounds for parameterized multifunctions between infinite-dimensional spaces. The obtained major result yields a new implicit function theorem and allows us to derive efficient conditions for semicontinuity and continuity of optimal value functions associated with parametric minimization problems subject to constraints governed by parameterized generalized equations.

Nonlinear analysis in p-vector spaces for single-valued 1-set contractive mappings

The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for 0 < p leq 1. More precisely, based on the fixed point theorem of single-valued continuous condensing mappings in locally p-convex spaces as the starting point, we first establish best approximation results for (single-valued) continuous condensing mappings, which are then used to develop new results for three classes of nonlinear mappings consisting of 1) condensing; 2) 1-set contractive; and 3) semiclosed 1-set contractive mappings in locally p-convex spaces. Next they are used to establish the general principle for nonlinear alternative, Leray–Schauder alternative, fixed points for nonself mappings with different boundary conditions for nonlinear mappings from locally p-convex spaces, to nonexpansive mappings in uniformly convex Banach spaces, or locally convex spaces with the Opial condition. The results given by this paper not only include the corresponding ones in the existing literature as special cases, but are also expected to be useful tools for the development of new theory in nonlinear functional analysis and applications to the study of related nonlinear problems arising from practice under the general framework of p-vector spaces for 0< p leq 1.Finally, the work presented by this paper focuses on the development of nonlinear analysis for single-valued (instead of set-valued) mappings for locally p-convex spaces. Essentially, it is indeed the continuation of the associated work given recently by Yuan (Fixed Point Theory Algorithms Sci. Eng. 2022:20, 2022); therein, the attention is given to the study of nonlinear analysis for set-valued mappings in locally p-convex spaces for 0 < p leq 1.

Remarks on Martio's conjecture

We introduce a certain integrability condition for the reciprocal of the Jacobian determinant which guarantees the local homeomorphism property of quasiregular mappings with a small inner dilatation. This condition turns out to be sharp in the planar case. We also show that every branch point of a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differential matrix of the mapping.

Scrambled sets and chain recurrence points of generic graph maps

In this paper two generic properties are presented for graph maps. Let be the space of continuous maps from the topological graph X into itself, equipped with the topology of uniform convergence. Then there is a residual subset such that for every , all the scrambled sets of f, as well as the set of chain recurrence points of f, are nowhere dense and of zero Hausdorff dimension.

On unique and non-unique fixed point in parametric N b −metric spaces with application

Abstract We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type b and η b −regularity in parametric N b -metric spaces to determine a unique fixed point, a unique fixed circle, and a greatest fixed disc. Further, we investigate the geometry of non-unique fixed points of a self mapping and demonstrate by illustrative examples that a circle or a disc in parametric N b −metric space is not necessarily the same as a circle or a disc in a Euclidean space. Obtained outcomes are extensions, unifications, improvements, and generalizations of some of the well-known previous results. We provide non-trivial illustrations to exhibit the importance of our explorations. Towards the end, we resolve the system of linear equations to demonstrate the significance of our contractions in parametric N b −metric space.

Some fixed points of multivalued maps in multiplicative metric spaces

In this manuscript, new fixed point theorems for multivalued maps, particularly α−ϕ contractions, in complete multiplicative metric spaces are proved. We further prove a fixed point theorem for multivalued mappings on a graph-equipped multiplicative metric space. Our results extend the result of Dosenovic et al. [4], and generalize the result of Ali et al. [2]. We included an example to validate our result.

On Fixed Points of Continuous Mappings Associated with Construction of Artificial Neural Networks

On Fixed Points of Continuous Mappings Associated with Construction of Artificial Neural Networks

Coupled fixed points of [formula omitted]-contractive mappings in partially ordered b-metric spaces

We aim to prove the existence and uniqueness of the fixed points for the self mappings satisfying generalized contractions involving altering distance functions in ordered metric type space. The results obtained in this work are generalizing some important findings in the literature and few illustrations are given to support the outcomes.

Birkhoff centre and backward limit points

We suggest one complete and one partial solution to the selected problems presented in the recently published article On Backward Attractors of Interval Maps (Hantáková and Roth (2021) [15]). Specifically we prove a conjecture proposing a characterisation of sets of β-limit points (i.e. limit points of all accumulation points of backward orbit branches of a specific point) for graph maps. We show that β-limit sets coincide with Birkhoff centre Rec(f)‾ and that the condition for a point to belong to its β-limit set is equivalent to belonging to the β-limit set of an other point.In the second part of the paper we deal with genericity of having all sα-limit sets closed and we prove that maps with not all sα-limit sets closed are dense in C0([0,1]), which partially solves an open problem also suggested in the aforementioned article.

On Common Fixed Point Theorems for Hybrid Mappings Satisfying Contractive Condition of Higher Degree and (CLR) Properties

In this study, we adopt an inequality of higher degree to acquire common fixed points for single and multi valued mappings with the help of (CLR) and (JCLR) properties. All of our results are strengthened with suitable examples.

On fixed points of locally and pointwise contractive set-valued maps with an application to the existence of Nash equilibrium in games

We establish the existence of fixed points for set-valued maps defined on metric spaces and satisfying a pointwise or a local version of Banach’s contraction property. As an application, we demonstrate the existence of Nash equilibrium in a general class of strategic games played on metric spaces of strategies.

The method for solving the extension of general of the split feasibility problem and fixed point problem of the cutter

This paper first introduces a new iterative method for weak and strong convergence theorem to demonstrate the estimation potential for a fixed point of the cutter and the finite general split feasibility problem. Consequently, the set of fixed points of a quasi-nonexpansive mapping and the finite general split feasibility problem, the constrained minimization problem, and the general constrained minimization problems are proved using our main results. Finally, we give two numerical examples to advocate our main results.