Type Fixed Point Theorem Research Articles

Some fixed point theorems in generalized parametric metric spaces and applications to ordinary differential equations

Abstract The objective of this work is the construction of `Boyd-Wong fixed point theorem’ in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value problem. Also an analogue of `Banach type fixed point theorem’ of generalized parametric metric space is proved and its application on the existence of a solution of first order periodic boundary value differential equation is examined.

On Some Applications of P-Contraction Fixed Point Theorems in Bipolar Metric Spaces

In this paper, we have discussed the P-contraction type fixed point theorems of covariant mappings in bipolar metric spaces, and we have shown an example which supports our results. Also we discussed applications to integral equations and Homotopy theory.

On some generalizations of Darbo- and Sadovskii- type fixed point theorems in Fréchet spaces

Integral equations form an essential part of nonlinear analysis. In many situations, when seeking solutions to such equations, we utilize fixed-point theorems. Among the most well-known and useful in this regard are the theorems of Darbo and Sadovskii, which generalize the classical results of Schauder and Tikhonov. These theorems have seen many generalizations. The aim of the paper is to strengthen (by weakening the assumptions) several known Darbo- and Sadovskii-type fixed-point theorems in the so-called power version for Fréchet spaces, which are particularly useful for studying the solvability of equations defined on an unbounded interval. A theorem on the existence of solutions to a nonlinear integral equation, illustrating the application of our main result, is also provided.

Solution of system of delay differential equations via new darbo type fixed point theorem in partially ordered banach space

Solution of system of delay differential equations via new darbo type fixed point theorem in partially ordered banach space

Leray Schauder Type Fixed Point Theorems in RWC-Banach Algebras and Application to Chandrasekhar Integral Equations

In this paper, the existence of fixed point results of Leray Schauder type for the sum and the product of nonlinear operators acting on RWC-Banach algebras under weak topology is proved. Our results are formulated in terms of a sequential characterization of the RWC-Banach algebra and the De Blasi measure of weak noncompactness. Application to Chandrasekhar Integral equations is also given.

Existence results and equilibrium stability conditions to fuzzy [formula omitted]-player generalized multiobjective games with application to economic equilibrium models

The purpose of this article is to study existence conditions and generic stability of solution sets to the fuzzy generalized multiobjective games in infinite dimensional spaces. First, we revisit a new class of the fuzzy generalized multiobjective games. Second, we introduce the concept of the extended Ci-quasi-concavity and establish existence conditions for fuzzy generalized multiobjective games using Browder type fixed point theorem in the noncompact cases. Third, we establish some sufficient conditions for generic solution stability conditions to such n-player multiobjective games under uncertainty. Finally, as a real-world application, we consider the special case of economic equilibrium models. Existence conditions and generic stability of solution sets for these real models are also obtained. The results obtained in this paper are new and different from the main results given by some authors in the literature.

Maia type fixed point theorems for multi-valued Feng-Liu operators

Maia type fixed point theorems for multi-valued Feng-Liu operators

A companion preorder to G-majorization and a Tarski type fixed-point theorem section: convex analysis

A companion preorder to G-majorization and a Tarski type fixed-point theorem section: convex analysis

A fractional order age-specific smoke epidemic model

This paper presents a nonlinear fractional mathematical model for the smoke epidemic that includes two age groups. To solve the smoke epidemic, the Atangana-Baleanu-Caputo fractional derivative is used. The Banach and Krasnoselskii type fixed point theorem is used to determine existence and uniqueness. We explored model stability using the Hyers-Ulam form of stability. Using Lagrange interpolation, the behaviour of the smoke epidemic of the 2-age group model is generated. The numerical simulation shows that the model has potential for both groups, and that age-specific interventions can be used to reduce smoking rates in the general population.

The Generalization of Ciric and Caristi Type Fixed Point Theorem

In this paper, we generalize the renowned Ciric and Caristi type fixed point theorem and some corollaries. Then we give an example to illustrate our result is really better than the theorem.

A Caristi type fixed point theorem which characterizes metric completeness

In this paper, we improve Caristi-Jachymski-Stein Jr and Banach-Caristi type fixed point theorems by relaxing the strong continuity assumption of the mapping with some weaker continuity notions. As an application, we show that the weaker version of the Caristi-Jachymski-Stein Jr fixed point theorem characterizes the completeness of the metric space and the Cantor intersection property.

On fixed points of generalized Kannan and Reich type contractive mappings

Kannan or Reich type strict contractive conditions do not ensure the existence of fixed points unless some strong conditions such as compactness of the space and continuity of the mapping are assumed. In this paper, our main aim is to investigate the existence of fixed point of generalized Kannan type contractive mappings in the setting of boundedly compact and T-orbitally compact metric spaces via orbital continuity. In addition to it, asymptotic regularity has been used to prove the Reich type fixed point theorem via altering distance functions. Supporting examples have been given to strengthen the hypotheses of our proved theorems.

Existence Results for Fractional Differential Equations Under Weak Topology Features

Using Krasnoselskii type fixed point theorem under the weak topology, we establish some sufficient conditions to ensure the existence of the weak solutions for kinds of initial value problems of fractional differential equations, involving Riemann-Liouville fractional derivative.

Componentwise localization of solutions to systems of operator inclusions via Harnack type inequalities

We establish compression-expansion type fixed point theorems for systems of operator inclusions with decomposable multivalued maps. The approach is vectorial allowing to localize individually the components of solutions and to obtain multiple solutions with multiplicity not necessarily concerned with all components of the solution. A general scheme of applicability of the theory is elaborated based on Harnack type inequalities and illustrated on systems of differential inclusions with one-dimentional ϕ-Laplacian.

On a boundary value problem for a class of fractional Langevin type differential equations in a Banach space

In this paper, we consider a boundary value problem for differential equations of Langevin type with the Caputo fractional derivative in a Banach space. It is assumed that the nonlinear part of the equation is a Caratheodory type map. Equations of this type generalize equations of motion in various kinds of media, for example, viscoelastic media or in media where a drag force is expressed using a fractional derivative. We will use the theory of fractional mathematical analysis, the properties of the Mittag-Leffler function, as well as the theory of measures of non-compactness and condensing operators to solve the problem. The initial problem is reduced to the problem of the existence of fixed points of the corresponding resolving integral operator in the space of continuous functions. We will use Sadovskii type fixed point theorem to prove the existence of fixed points of the resolving operator. We will show that the resolving integral operator is condensing with respect to the vector measure of non-compactness in the space of continuous functions and transforms a closed ball in this space into itself.

Kaleva-Seikkala’s Type Fuzzy b -Metric Spaces and Several Contraction Mappings

In this paper, we introduce the concept of Kaleva-Seikkala’s type fuzzy b -metric spaces as a generalization of the notion of b -metric spaces and fuzzy metric spaces. In such spaces, we establish Banach type, Reich type, and Chatterjea type fixed-point theorems, which improve the relevant results in fuzzy metric spaces. Two technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. Finally, various applications are given to testify the fact that our main theorems extend the cases of b -metric spaces.

Fixed point theorems on an orthogonal metric space using Matkowski type contraction

The purpose of this paper is to prove Boyd-Wong and Matkowski type fixed point theorems in orthogonal metric space which was defined by M.E. Gordji in 2017 and is an extension of the metric space. Some examples are established in support of our main results. Finally, we apply our results to establish the existence of a unique solution of a periodic boundary value problem.

Coupled system of $\psi$--Caputo fractional differential equations without and with delay in generalized Banach spaces

The main objective of this research manuscript is to establish various existence and uniqueness results as well as the Ulam--Hyers stability of solutions to a Coupled system of $\psi$--Caputo fractional differential equations without and with delay in generalized Banach spaces. Existence and uniqueness results are obtained by applying Krasnoselskii's type fixed point theorem, Schauder's fixed point theorem in generalized Banach spaces, and Perov's fixed point theorem combined with the Bielecki norm. While Urs's approach is used to analyze the Ulam--Hyers stability of solutions for the proposed problem. Finally, Some examples are given to illustrate the obtained results.

Feng-Liu type fixed point theorems for w-distance spaces and applications

In this article, we study Feng-Liu [Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), 103-112.] type fixed point theorems and present some new results for multi-valued mappings in metric spaces using the concept of ?-distance. We also discuss, some non-trivial examples to illustrate facts. Finally, we present applications of our results to integral inclusions and non-linear matrix equations. An example is given, together with convergence and error analysis, as well as average CPU time analysis and visualization of solution in surface plot.

A unification of Geraghty type and Ciric type fixed point theorems

In the framework of metric spaces, we introduce the concept of Geraghty-Ciric type contractions and show the existence and uniqueness of the fixed point of such mappings. This result improves and unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) and Ciric (Proc. Amer. Math. Soc. 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. In addition, two illustrative examples are provided to indicate the validity of the obtained results.