Integral Inclusion Research Articles

Analytical Solutions for a Nonlinear Quadratic Delayed Functional Integral Inclusion With Feedback Control on the Real Half-Line

Let E be a reflexive Banach space. In this research, we are interested in the solvability of the nonlinear quadratic delayed functional integral inclusion (NQDFII) with a feedback control condition on the real half-axis. Our examination is found within the space BC(R+, E) of bounded continuous functions on the real half-axis R+ and takes values in a reflexive Banach space E beneath the assumption that the set-valued function G satisfy Lipschitz condition in E. The base we depend on in this study is the procedure related to a measure of noncompactness in the space BC(R+, E) by a given norm of continuity and applying Darbo’s fixed point theorem. Moreover, the asymptotic stability of the solution and the asymptotic dependency of the solution on the set of selections SG will be examined. Also, we give an example to illustrate the adequacy and esteem of our comes about.

Integrable Solutions and Continuous Dependence of a Nonlinear Singular Integral Inclusion of Fractional Orders and Applications

Let E be a reflexive Banach space. In this article we study the existence of integrable solutions in the space of all lesbesgue integrable functions on E, L1([0,T],E), of the nonlinear singular integral inclusion of fractional orders beneath the assumption that the multi-valued function G has Lipschitz selection in E. The main tool applied in this work is the Banach contraction fixed point theorem. Moreover, the paper explores a qualitative property associated with these solutions for the given problem such as the continuous dependence of the solutions on the set of selections S1G(τ,x(τ)). As an application, the existence of integrable solutions of the two nonlocal and weighted problems of the fractional differential inclusion is investigated. We additionally provide an example given as a numerical application to demonstrate the effectiveness and value of our results.

Ćirić-type generalized [formula omitted]-contractions with integral inclusion in super metric spaces

This study aims to explore Ćirić-type generalized F-contractions, almost F-contractions, and the combination of these contractions in the framework of super metric spaces. These generalizations are significant because they hold where the usual metric conditions mayn’t be fulfilled. Using the iteration method, fixed point results have been obtained for these contractions, and through examples and applications to integral inclusions and contractions, we extend existing literature significantly. This extension offers new insights and demonstrates practical relevance.

A common fixed point result for multi-valued mappings in Hausdorff modular fuzzy b-metric spaces with application to integral inclusions

Abstract The modular fuzzy b-metric space is defined in this study, and we are interested in proving a general common fixed point theorem for a pair of multi-valued mappings in Hausdorff modular fuzzy b-metric spaces. The work generalizes the findings in [H. Kerim, W. Shatanawi, A. Tallafha and T. A. M. Shatnawi, Fixed point theorems on modular fuzzy metric spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 2022, 1, 47–58] and produce additional specific findings that are supported by examples. An application to prove the existence of an integral inclusion equation’s solution is shown to demonstrate the importance of our result.

Set-valued mappings: fixed point results with $\beta$-function and some applications

Via the so-called $\beta$-function, some fixed-point results for nonexpansive set-valued mappings are obtained. In this study, the results are considered in the context of complete metric spaces which are neither uniformly convex nor compact. Our theorems extend, unify, and improve several recent results in the existing literature. In the end, we apply our new results to ensure the existence of a solution for a nonlinear integral inclusion. Moreover, we approximate the fixed point by a faster iterative process.

Stability and dependency of the solution of a nonlinear quadratic functional integral inclusion with distributed delay

Stability and dependency of the solution of a nonlinear quadratic functional integral inclusion with distributed delay

Strong Solutions and Mild Solutions for Sturm-Liouville Differential Inclusions

Existence results for a Cauchy problem driven by a semilinear differential Sturm-Liouville inclusion are achived by proving, in a preliminary way, an existence theorem for a suitable integral inclusion. In order to obtain this proposition we use a recent fixed point theorem that allows us to work with the weak topology and the De Blasi measure of weak noncompactness. So we avoid requests of compactness on the multivalued terms. Then, by requiring different properties on the map p involved in the Sturm-Liouville inclusion, we are able to establish the existence of both mild solutions and strong ones for the problem examinated. Moreover we focus our attention on the study of controllability for a Cauchy problem governed by a suitable Sturm-Liouville equation. Finally we precise that our results are able to study problems involving a more general version of a semilinear differential Sturm-Liouville inclusion.

Fixed Point Theorems for Set-Valued Contractions in Metric Spaces

In this paper, the concepts of Wardowski-type set-valued contractions and Işik-type set-valued contractions are introduced and fixed point theorems for such contractions are established. A positive answer to the open Question is given. Examples to support main theorems and an application to integral inclusion are given.

Comprehensive Approach of an Implicit Hybrid Urysohn–Stieltjes Integral Inclusions via Fractal Differential Constraint

This investigation establishes the solvability of an implicit hybrid nonlinear Urysohn–Stieltjes type (IHU‐S) integral inclusion. Some sufficient conditions are assumed to prove qualitative features for the solution for this class of inclusions. A comprehensive discussion and analysis, including an example and an application, is presented to illustrate our results.

Multivalued relation-theoretic weak contractions and applications

Abstract In this article, we discuss the relation theoretic aspects of multivalued weakly contractive mappings to prove fixed point results in the setting of metric spaces endowed with a certain binary relation. Our newly proved results generalize, extend, unify, enrich, sharpen and improve some well-known fixed point theorems of existing literature to the case of multivalued and contractive notion. We also incorporated an example and an application to find the solution of a Volterra-type integral inclusion.

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis

In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in BC(R+). In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions.

Танец и личность

The article is devoted to the problem of personal involvement in dance activity. The author applies an interdisciplinary research methodology: on the one hand, a semiotic analysis of the dance language is carried out and the features of the dance sign are considered, on the other hand, a psychological description of the dancer’s personality is given, a psychological portrait is created. According to the methodology of the cultural-historical approach, the sign is taken in its instrumental function and orientation. The author puts forward a hypothesis about the dual orientation of the dance movement as an expressive language: orientation on the viewer as a visual component of the sign and on the dancer himself through the kinesthetic component. The material of dance as a type of artistic activity is the body of the dancer, which undergoes reinterpretation and symbolization. Not only the body, but also the whole personality can become the material of dance, it can be included and transformed in the course of the dance activity. The bi-directionality of the dance sign can lead to a discrepancy, a rupture of the function of the dance movement, which is expressed in an object relation to one’s own body, in strict control of movements and the non-involvement of the emotional and sensual sphere of the individual in the dance activity. Stage forms of dance contribute more to this discrepancy, developing mainly motor technique in isolation from the semantic side of movement and focusing on the visual expressiveness of dance. On the other hand, ceremonial, sacred, ritual dances, many forms of modern free dance contribute to the integral inclusion of a person in the dance and are aimed at transforming the personality in plastic action. On the basis of biographical material, the destinies of outstanding dancers and dance teachers are analyzed. It is shown how an object attitude to one’s own body and one’s own personality can lead to an internal split and loss of subjectivity. A contradiction may arise between a person’s experience in dance and her/his behavior in real life. It is removed under the condition that a person carries out a transformative activity – work on himself/herself.

Hybrid Fixed Point Theorems of Fuzzy Soft Set-Valued Maps with Applications in Integral Inclusions and Decision Making

A lot of work has been completed in efforts to extend the notions of soft set and fuzzy soft set and their applications to other domains. However, neither of the two concepts has been examined in the study of functional equations in b-metric spaces. Given this background information, this paper proposes the idea of b-hybrid fuzzy soft contraction in b-metric space and investigates new criteria for the existence of fixed points for such mappings. The significance of the obtained principal result lies in the fact that the contractive inequalities can be specialized in various ways, depending on the choice of the parameters, thereby making it possible to unify, deduce, and refine several corresponding results. To motivate further studies in the directions studied herein, two applications regarding decision-making problems and an existence theorem of integral inclusion are considered, using fuzzy soft set-valued maps.

Chatterjea type theorems for complex valued extended $ b $-metric spaces with applications

<abstract><p>In this article, we establish common $ \alpha $ -fuzzy fixed point theorems for Chatterjea type contractions involving rational expression in complex valued extended $ b $-metric space. Our results generalize and extend some familiar results in the literature. Some common fixed point results for multivalued and single valued mappings are derived for complex valued extended $ b $-metric space, complex valued $ b $-metric space and complex valued metric space as consequences of our leading results. As an application, we investigate the solution of Fredholm integral inclusion.</p></abstract>

Solution of integral equations for multivalued maps in fuzzy $ b $-metric spaces using Geraghty type contractions

<abstract><p>In this article, the notion of Hausdorff fuzzy $ b $-metric space is studied. Some fixed point results for multivalued mappings using Geraghty type contractions in $ G $-complete fuzzy $ b $-metric spaces are established. To strengthen the results, an illustrative example is furnished. A fuzzy integral inclusion is constructed as an application of fixed point result which shows the validity of the proved results. The presented outcomes are the generalization of the existing results in literature.</p></abstract>

Исследование краевой задачи для дифференциального включения

The boundary value problem with respect to an absolutely continuous function x:[a,b]→R^n for the differential inclusion F(t,x,x ̇,x ̇)∋0,t∈[a,b], with the condition αx(a)+βx(b)=γ ̃ and additional restriction on the derivative of the desired function (Lx)(t)≐x ̇(t)-λx(t)∈B(t), t∈[a,b] is under discussion. It is assumed that the boundary value problem with the same conditions for the linear differential equation Lx=y is uniquely solvable for any summable function y. Using Green’s function of this «auxiliary» linear boundary value problem, the original problem is reduced to an equivalent integral inclusion with respect to the summable function x ̇. To the inclusion obtained, the results on operator inclusion with an orderly covering multivalued mapping are applied. In the first section of the work, the information about multivalued mappings of partially ordered spaces used in this study is given. In the main section of the work, conditions for the existence and estimates of solutions to the boundary value problem under investigation are obtained in the form of a statement similar to Chaplygin’s theorem on differential inequality. These results are illustrated by an example of studying a periodic boundary value problem for a differential equation which is not resolved with respect to the derivative.

Q-ROF mappings and Suzuki type common fixed point results in b-metric spaces with application

In the present paper the concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and q-rung ( alpha ,beta ) -cuts are introduced. Some common fixed point results for q-ROF mappings are presented in b-metric spaces using Suzuki-type contractive conditions. Examples in support of obtained results are also presented. We have also presented an application of our result for the existence of solution of nonlinear fractional integral inclusion. The results are of their own kind in the literature of q-ROF sets and will pave the way for further research in the area.

Existence of multiple solutions for a wide class of differential inclusions†

AbstractWe give a unified approach to study the existence of multiple positive solutions of nonlinear differential inclusions of the form subject to various nonlocal boundary conditions. We study these problems via a perturbed integral inclusion of the form .

Multivalued FG-Contraction Mappings on Directed Graphs

In this paper, we study generalized FG-contraction conditions for a pair of mappings defined on a family of subsets of a metric space endowed with a directed graph, and discuss coincidence and common fixed point results relaxing the continuity of mappings. The given notions and results are exemplified by suitable models. We apply our results to the problem of existence of solutions of a Fredholm integral inclusion.