Types Of Maps Research Articles

Control Functions in G-Metric Spaces: Novel Methods for θ-Fixed Points and θ-Fixed Circles with an Application

The purpose of this paper is to present some new contraction mappings via control functions. In addition, some fixed point results for Θ,α,θ,Ψ contraction, rational Θ,α,θ,Ψ contraction and almost Θ,α,θ,Ψ contraction mappings are obtained. Moreover, under contraction mappings of types (I), (II), and (III) of Θ,θ,Ψυ0, several fixed circle solutions are provided in the setting of a G-Metric space. Our results extend, unify, and generalize many previously published papers in this direction. In addition, some examples to show the reliability of our results are presented. Finally, a supporting application that discusses the possibility of a solution to a nonlinear integral equation is incorporated.

On some contractive mappings and a new version of implicit function theorem in topological spaces

Study on existence of fixed points of contraction and contractive (type) mappings in topological spaces is a challenging task. The main goal of this article is to deal with this challenging task. To achieve our goal, we define two new contractive type mappings, namely, h-A-contractive and h-A1-contractive mappings on a topological space X, where h : X ? X ? R+ is a function and A, A1 are two collections of implicit functions. Then, we obtain some fixed point results concerning such contractive type mappings. Finally, as an application of one of the above mentioned fixed point results, we obtain a newer version of the implicit function theorem in topological spaces.

Representation of exact trajectory solutions for chaotic one-dimensional maps in Schroder form

Purpose of the article is to illustrate the genesis, meaning and significance of the functional Schroder equation, introduced in the theory of iterations of rational functions, for the theory of deterministic chaos by analytical calculations of exact trajectory solutions, invariant densities and Lyapunov exponents of one-dimensional chaotic maps. We demonstrate the method for solving the functional Schroder equation for various chaotic maps by passing to a topologically conjugate mappings, for which finding the exact trajectory solution is a simpler mathematical procedure. Results of the analytical solution of the Schroder equation for 12 chaotic mappings of various types and the calculation of the corresponding expressions for exact trajectory solutions, invariant densities and Lyapunov exponents are presented. Conclusion is made about the methodological expediency of formulating and solving the Schroder equations by the study of the dynamics of one-dimensional chaotic mappings.

Fixed Point Theorems for Compatible Mappings of Type () in Intuitionistic Fuzzy Metric Space

Fixed Point Theorems for Compatible Mappings of Type () in Intuitionistic Fuzzy Metric Space

Fixed point theorems for self mappings in generalized metric spaces

In this paper a fixed point theorem in D- metric space using contractive type mappings is discussed. This work is an extension of the result obtained in [2].

Existence and convergence results for a class of non-expansive type mappings in Banach spaces

In this article, we concentrate on common fixed points of a pair of generalized non-expansive mappings, viz., generalized ?-Reich-Suzuki non-expansive mappings. In this sequel, we introduce the three step Abbas-Nazir iterative algorithm for a pair of mappings. Then we obtain some results related to weak and strong convergence of sequences, satisfying this iterative algorithm, to obtain the common fixed points of two generalized ?-Reich-Suzuki non-expansive mappings. Finally, we compare the convergence rate of our iteration technique to that of some well-known iteration techniques by some constructive numerical examples.

Geraghty-Ciric type mappings with an application

Geraghty-Ciric type mappings with an application

Approximating Finite Families of Resolvents of Convex Functions and Fixed Point Problem of Demicontractive Type Mappings

Approximating Finite Families of Resolvents of Convex Functions and Fixed Point Problem of Demicontractive Type Mappings

Some approximate fixed point results for various contraction type mappings

Some approximate fixed point results for various contraction type mappings

Fixed points of asymptotically nonexpansive type mappings

Fixed points of asymptotically nonexpansive type mappings

On Some Fixed Point Theorems for $\mathcal{G} (\Sigma, \vartheta, \Xi )-$Contractions in Modular $b-$Metric Spaces

This article aims to specify a new $C-$class function endowed with altering distance and ultra altering distance function via generalized $\Xi -$contraction, which is called the $\mathcal{G}\left( {\Sigma ,\vartheta ,\Xi } \right) - $contraction in modular $b-$metric spaces. Regarding these new contraction type mappings, the study includes some existence and uniqueness theorems, and to indicate the usability and productivity of these results, some applications related to integral type contractions and an application to the graph structure.

A Focus on Types of Compatible Mappings in \(S\)-metric Space

In this article, we study unique common fixed point theorems for four self mappings in S-metric space using generalized concepts of compatible mappings such as compatible mappings of type (A), type (B) and type (C). Our results are generalizing the theorems proved by Sedghi et al. (Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018), 137 – 143) in metric space.

Triple Invariant Point Theorems with PPF Dependence for Contractive Type Mappings

In this paper, some results concerning the existence and uniqueness of triple invariant point with PPF dependence for non linear mapping in partially ordered complete metric spaces using the domain space \(C[[a,b],E]\) that is distinct from the range \(E\). Our results generalize and extend recent coupled invariant point theorems with PPF dependence founded by Drici et al. (Fixed point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Analysis 67 (2007), 641 – 647).

Generalized Contractions on Extended \(b\)-Metric Space Endowed With a Graph

The goal of this study is to obtain fixed point and coincidence point results for interpolative Hardy Rogers and Ćirić-Reich-Rus type contractive type mappings in an extended $b$-metric space, which is a generalization of \(b\)-metric space, based on Errai et al. (Some new results of interpolative Hardy-Rogers and Ćirić-Reich-Rus type contraction, 2021 (2021), Article ID 9992783). We present a variety of examples which backs up our findings.

Solution of fractional integral equations via fixed point results

In this paper, we introduce two new concepts of F-contraction, called dual F^{*}-weak contraction and triple F^{*}-weak contraction, which generalize the existing contractions in the sense of Wardowski, Jleli and Samet as well as Skof. These new generalizations embed their roots in the aim devoted to extending the generalized Banach contraction conjuncture to the class of F-contraction type mappings with the use of multiple F-type functions. Furthermore, we establish the existence of a unique fixed point for such contractions under certain conditions. Fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates that can be expressed as functions of one independent variable. We apply our main result to weaken certain conditions on the fractional integral equations. Finally, we discuss the significance of our obtained results in comparison with certain renowned ones in the literature.

Existence of common fixed point in Kannan F-contractive mappings in quasi-partial b-metric space with an application

The purpose of this study is to demonstrate results on fixed point theory in quasi-partial b-metric space recognizing a new type of mapping, which is a blend of F-contraction and Kannan contraction, and to establish the fixed point results in F-expanding type mappings. Additionally, the obtained results are the application of the contractive mappings to functional equations. Furthermore, Mathematica software is used to demonstrate the 3D shapes of the examples discussed here.

A COMMON FIXED POINT THEOREM IN MENGER SPACE WITH WEAKLY COMPATIBLE MAPPINGS OF TYPE (P)

We define weakly compatible mappings of type $(P)$ in Menger space and establish the common fixed point theorem for four self-mappings in this space with an appropriate example. Our result generalizes and extends a number of similar results in the literature.

A COMMON FIXED POINT THEOREM IN MENGER SPACE WITH COMPATIBLE MAPPING OF TYPE (K)

The notion of compatible mappings of type $(K)$ in metric space has been introduced by K. Jha, V. Popa, and K.B. Manandhar in 2014. In this paper, we use Meir-Keeler contractive type condition and establish a common fixed point theorem in Menger probabilistic metric space by using compatible mappings of type $(K)$. Our results generalize and improve several similar known results in the literature.

SOME COMMON FIXED POINT THEOREMS FOR FUZZY TYPE RATIONAL CONTRACTIVE MAPPINGS IN HILBERT SPACES

Heilpern [1] introduced and studied the concept of fuzzy mappings and proved some fixed point theorems for fuzzy contraction mappings. Subsequently several authors studied and generalized the existence of fixed points and common fixed points of fuzzy mappings satisfying various contraction type conditions in metric spaces (see [2],[3],[4],[5], and others). Dutta P.N and Choudhury B.S [6] studied some fixed points for fuzzy mappings in Hilbert spaces. Further Shrivastava R. et al. [7] proved a common fixed point theorem for fuzzy type mapping in Hilbert space. Motivated by the results in [6, 7], we prove three common fixed point theorems for fuzzy rational type mappings in Hilbert spaces. The results extend and generalize many previous known results in the literature.

Generalized $$\alpha $$-$$\psi $$ contractive type mappings and related coincidence fixed point theorems with applications

Generalized $$\alpha $$-$$\psi $$ contractive type mappings and related coincidence fixed point theorems with applications