Integral Inclusions Research Articles

Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions

The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}-contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}. Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi$$\\end{document} and ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document} and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

Rational-type contractions and their applications in extended b-metric spaces

This paper examines the analysis of some rational-type contractions within the context of extended b-metric spaces, establishes a theoretical foundation for rational-type contractions and demonstrates their application in Volterra integral inclusions and Urysohn integral equations. Some examples are provided for the authenticity of the findings.

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.

New L-fuzzy fixed point techniques for studying integral inclusions

The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions.

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.

Fixed point theory for F-set-contraction multimaps and application to a system of integral inclusions

Fixed point theory for F-set-contraction multimaps and application to a system of integral inclusions

Existence results for nonexpansive multi-valued operators and nonlinear integral inclusions

Existence results for nonexpansive multi-valued operators and nonlinear integral inclusions

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.

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.

Retracted: A Solution of Fredholm Integral Inclusions via Suzuki‐Type Fuzzy Contractions

Retracted: A Solution of Fredholm Integral Inclusions via Suzuki‐Type Fuzzy Contractions

Existence of Urysohn and Atangana–Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators

This paper aims to prove that the solution of the integral equation systems exists via the concepts of fixed point and multi-valued operators. For this purpose, at first, some new theoretical results are presented and proved for the existence of a common fixed point for a pair of multi-valued operators. The multi-valued operators are αℂ-admissible and hold a new generalized contractive condition in complex-valued double-controlled metric spaces. In applying the considered generalized contractive condition on multi-valued operators, an important principle of complex numbers has complied, which is inadvertently neglected in some research This unneglectable principle is that the maximum of two complex numbers is not necessarily one of them; Rather, it can be greater than both. Thus, in our applied contractive condition, satisfying the contraction condition is considered with any member of the assumed set instead of the set maximum. Consequently, the presented results in this work improve and generalize some results mentioned in the literature. In the Applications section, two existence theorems for the solution of Urysohn integral equations system and Atangana–Baleanu fractional integral inclusions system are provided and proved based on our obtained theoretical results. Finally, analytical and numerical examples are provided to confirm the applicability of the obtained theoretical results.

Hybrid Fuzzy Contraction Theorems with Their Role in Integral Inclusions

The focus of this paper is to establish a new concept of b-hybrid fuzzy contraction regarding the study of fuzzy fixed-point theorems in the setting of b-metric spaces. This idea harmonizes and refines several well-known results in the direction of point-valued, multivalued, and fuzzy-set-valued maps in the comparable literature. To attract new researchers to this field, some important results are shown to be corollaries. Moreover, a result is presented to establish sufficient conditions for the existence of solutions of integral inclusion of Fredholm type. Lastly, illustrations are presented to validate the suppositions of the given theorems.

Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps

Abstract In this paper, new common fuzzy fixed point theorems for sequence of fuzzy set-valued maps in the framework of complete b-metric spaces are established. Consequently, corresponding fixed point theorems in the setting of point-to-set-valued and single-valued mappings are deduced. A few nontrivial examples which dwell upon the generality of our results are provided. Moreover, following the fact that most available Ulam-Hyers type stability results deal with crisp mappings, we initiate the study of stability and well-posedness of functional inclusions involving fuzzy set-valued maps. It is well-known that solution of any functional inclusion is a subset of an appropriate ambient space. With this information, fuzzy fixed point problem for which the right-hand-side is a cut set of a fuzzy set-valued map is introduced. Furthermore, sufficient conditions for existence of solutions of Cantilever Beam Problem and integral inclusions are investigated to indicate the usability of our obtained results.

Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings

The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractional integral inequalities are also proved via Riemann–Liouville fractional integral operator, where integrands are fuzzy-interval-valued functions. To prove the validity of our main results, some of the nontrivial examples are also provided. As specific situations, our findings can provide a variety of new and well-known outcomes which can be viewed as applications of our main results. The results in this paper can be seen as refinements and improvements to previously published findings.

Inclusions Involving Interval‐Valued Harmonically Co‐Ordinated Convex Functions and Raina’s Fractional Double Integrals

The aim of this article is to obtain some new integral inclusions essentially using the interval‐valued harmonically co‐ordinated convex functions and κ‐Raina’s fractional double integrals. To show the validity of our theoretical results, we also give some numerical examples.

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.

New fixed point theorems for countably condensing maps with an application to functional integral inclusions

Abstract This paper presents new fixed point theorems for 2 × 2 block operator matrix with countably condensing or countably 𝓓-set-contraction multi-valued inputs. Our theory will then be used to establish some new existence theorems for coupled system of functional differential inclusions in general Banach spaces under weak topology. Our results generalize, improve and complement a number of earlier works.

On the fractional integral inclusions having exponential kernels for interval-valued convex functions

On the fractional integral inclusions having exponential kernels for interval-valued convex functions

On Suzuki and Wardowski-Type Contraction Multivalued Mappings in Partial Symmetric Spaces

The purpose of this paper is to provide some fixed-point results for Suzuki and Wardowski-type contraction multivalued mappings in partial symmetric spaces. We give some examples to support and substantiate the developed notions and obtained results. Also, we use one of our main results to establish the existence and uniqueness of the solution for a system of integral inclusions.

Common fixed point theorems for multivalued mappings in b-metric spaces with an application to integral inclusions

Common fixed point theorems for multivalued mappings in b-metric spaces with an application to integral inclusions