Mappings In Metric Spaces Research Articles

Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of g -interpolative Hardy–Rogers type contractions in b -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.

A Common Fixed Point Theorem for Generalised F -Kannan Mapping in Metric Space with Applications

This paper is aimed at proving a common fixed point theorem for F -Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results.

Local behavior of mappings of metric spaces with branching

The local behavior of mappings with the inverse Poletsky inequality between metric spaces is studied. The case where one of the spaces satisfies the condition of weak sphericalization, is similar to the Riemannian sphere (extended Euclidean space), and is locally linearly connected under a mapping is considered. It is proved that the equicontinuity of the corresponding families of mappings of two domains, one of which is a domain with a weakly flat boundary, and another one is a fixed domain with a compact closure, the corresponding weight in the main inequality being supposed to be integrable.

On New χ -Fixed Point Results for λ − Υ , χ -Contractions in Complete Metric Spaces with Applications

The main aim of this work is to introduce the new concept of λ − Υ , χ -contraction self-mappings and prove the existence of χ -fixed points for such mappings in metric spaces. Our results generalize and improve some results in existing literature. Moreover, some fixed point results in partial metric spaces can be derived from our χ -fixed points results. Finally, the existence of solutions of nonlinear integral equations is investigated via the theoretical results in this work.

Design Trend Forecasting by Combining Conceptual Analysis and Semantic Projections: New Tools for Open Innovation

In this paper, we describe a new trend analysis and forecasting method (Deflexor), which is intended to help inform decisions in almost any field of human social activity, including, for example, business, art and design. As a result of the combination of conceptual analysis, fuzzy mathematics and some new reinforcing learning methods, we propose an automatic procedure based on Big Data that provides an assessment of the evolution of design trends. The resulting tool can be used to study general trends in any field—depending on the data sets used—while allowing the evaluation of the future acceptance of a particular design product, becoming in this way, a new instrument for Open Innovation. The mathematical characterization of what is a semantic projection, together with the use of the theory of Lipschitz functions in metric spaces, provides a broad-spectrum predictive tool. Although the results depend on the data sets used, the periods of updating and the sources of general information, our model allows for the creation of specific tools for trend analysis in particular fields that are adaptable to different environments.

On Equicontinuous Families of Mappings of Metric Spaces

We obtain analogs of the results on equicontinuity of families of quasiregular mappings that take no values from a fixed continuum. We prove that these families are equicontinuous whenever the quasiconformality characteristics of the mappings have finite mean oscillation at every inner point. In this context, we also prove the equicontinuity of generalized quasiisometries of Riemannian manifolds.

Fixed point results for materials research

In this paper, we establish a new Class category of non expansive mappings in metric space which is wider than the class category of mappings satisfying contractive condition (CC). Special properties and various fixed point results for these mappings in metric space are obtained here. Also we discussed the results and examples of the convergence of some iteration schemes to the fixed point in metric space. Obtained results are useful in material research as well as in image processing.

Approximate fixed points and fixed points for multi-valued almost E-contractions

Abstract In this paper, we introduce the concept of multi-valued almost E-contractions. We then present some approximate fixed point and fixed point results for such mappings in metric spaces. Our results generalize and improve several well-known results in literature. We also provide several illustrative examples to compare our findings with some earlier results. An application to homotopy theory is given.

Local competing in interpolation problems

A simple example illustrates the insufficiency of the known approaches to interpolation in the problem of recovering a function from a few given specific values that clearly convey the form. A local choice between polynomial and rational local interpolants, which minimizes the local interpolant’s errors at the nearest external nodes from one or different sides, complements the known approaches. It combines the extreme computational simplicity of local interpolants with the thorought selection of them. The principles of constructing the algorithm are formulated in general terms for mappings of metric spaces. They provide accurate (with rare exceptions) reconstruction of mappings that locally coincide with some of the given possible interpolants. In the one-dimensional case, the two-stage algorithm guarantees the continuity of the interpolant and accurately reconstructs polynomials of small degree, simple rational functions with a linear denominator, and broken lines of long links with knots at the ends when these requirements do not contradict each other. An additional parameter allows you to replace the exact restoration of polylines with the required smoothness of interpolation.

Local behavior of mappings of metric spaces with branching

The local behavior of mappings with the inverse Poletsky inequality between metric spaces is studied. The case where one of the spaces satisfies the condition of weak sphericalization, is similar to the Riemannian sphere (extended Euclidean space), and is locally linearly connected under a mapping is considered. It is proved that the equicontinuity of the corresponding families of mappings of two domains, one of which is a domain with a weakly flat boundary, and another one is a fixed domain with a compact closure, the corresponding weight in the main inequality being supposed to be integrable.

Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

Fixed Circle and Fixed Disc Results for New Types of Θc-Contractive Mappings in Metric Spaces

In this manuscript, we introduce the notions of various types of Θc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings, which generalize many results of invariance and transformations in the literature.

Preservation of the Existence of Zeros in a Family of Set-Valued Functionals and Some Consequences

A theorem on the preservation of the existence of zeros under the change of the parameter in a one-parameter family of $$(\alpha,\beta)$$ -search functionals on an open subset of a metric space is proved. The following corollaries of this theorem are presented: on the preservation of the existence of preimages of a given closed subspace in a parametric family of multivalued mappings of metric spaces; on the preservation of the existence of coincidence points in a finite collection of two or more families of multivalued mappings of metric spaces; on the preservation of the existence of common fixed points in a collection of families of multivalued mappings to itself of a metric space. As a simple particular case, the Frigon–Granas theorem (1994) on fixed points of a contraction family of multivalued mappings is obtained.

Comparison Method for Studying Equations in Metric Spaces

We consider the equation $$G(x,x)=y$$ , where $$G\colon X\times X\to Y$$ and $$X$$ and $$Y$$ are metric spaces. This operator equation is compared with the “model” equation $$g(t,t)=0$$ , where the function $$g\colon \mathbb{R}_+\times \mathbb{R}_+ \to\mathbb{R}$$ is continuous, nondecreasing in the first argument, and nonincreasing in the second argument. Conditions are obtained under which the existence of solutions of this operator equation follows from the solvability of the “model” equation. Conditions for the stability of the solutions under small variations in the mapping $$G$$ are established. The statements proved in the present paper extend the Kantorovich fixed-point theorem for differentiable mappings of Banach spaces, as well as its generalizations to coincidence points of mappings of metric spaces.

Fixed Point Results of Expansive Mappings in Metric Spaces

In this study, we introduce the concept of θ-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for θ-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved.

Several Theorems on Single and Set-Valued Prešić Type Mappings

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Prešić type almost F-contractive operators is not included in Prešić type class of set-valued Prešić type almost contractive operators.

Approximation of BV by SBV functions in metric spaces

In a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we show that functions of bounded variation (BV functions) can be approximated in the strict sense and pointwise uniformly by special functions of bounded variation, without adding significant jumps. As a main tool, we study the variational 1-capacity and its BV analog.

Approximating Stationary Points of Multivalued Generalized Nonexpansive Mappings in Metric Spaces

In this research, under some appropriate conditions, we approximate stationary points of multivalued Suzuki mappings through the modified Agarwal-O’Regan-Sahu iteration process in the setting of 2-uniformly convex hyperbolic spaces. We also provide an illustrative numerical example. Our results improve and extend some recently announced results of the current literature.

Common Fixed Point of Three Contractive Type Mappings in Metric Spaces

Common Fixed Point of Three Contractive Type Mappings in Metric Spaces

Common fixed points for generalized $$\left( \alpha {-}\psi \right)$$-Meir–Keeler–Khan mappings in metric spaces

In this article, we prove a common fixed point results for two pairs of weakly compatible self-mappings in a complete metric space satisfying $$\left( \alpha ,\psi \right)$$ -Meir–Keeler–Khan type contractive condition. We present an example to illustrate main result. Some other results and consequences are also given. These results generalize some classical results in the current literature.