4,466 Results Found

In this study, we defined a kind of Fourier expansion of set-valued square-integrable functions. In fact, we have seen that the classical Fourier basis also constitutes a basis for the Hilbert quasilinear space $L_2(\left[-\pi ,\pi \right],\Omega \left(\mathbb{C}\right))$ of $\&Ome$...

A theory for set-valued functions is developed, which are translative with respect to a linear operator. It is shown that such functions cover a wide range of applications, from projections in Hilbert spaces, set-valued quantiles for vector-valued ra...

The decomposition integrals of set-valued functions with regards to fuzzy measures are introduced in a natural way. These integrals are an extension of the decomposition integral for real-valued functions and include several types of set-valued integ...

The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function $F:X\to cc$...

Fault diagnosis is crucial for ensuring the reliability and safety of wind energy conversion systems (WECSs). However, existing methods are often specific to components or specific types of wind turbines and face challenges, such as difficulty in thr...

In this paper, by using the normal subdifferential and equilibrium-like function we first obtain some properties for K-preinvex set-valued maps. Secondly, in terms of this equilibrium-like function, we establish some sufficient conditions for the exi...

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. Th...

This paper introduces and studies alternating points of two set-valued mappings acting between two 0-complete strong partial b-metric spaces. An alternating point is a mutually compatible pair of states, each of which belongs to the image of the othe...

We address the problem of approximating a set-valued function F, where $F:[a,b]\to K\left({\mathbb{R}}^d\right)$ given its samples ${\left\{F(a+ih)\right\}}_{i=0}^N$, with $h=(b-a)/N$. We revisit an existing method that approximates set-valued functions by interpolating signed-distance fun...

We present existing results and properties for the solutions of some vector equilibrium problems with set-valued functions in the case of a vector space ordered by a cone with some “interiority” properties. Some applications concerning th...

In this paper, we study the structure of trajectories of discrete disperse dynamical systems with a Lyapunov function which are generated by set-valued mappings. We establish a weak version of the turnpike property which holds for all trajectories of...

Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on t...

This paper establishes a local fixed point theorem for multivalued mappings in zero-complete strong partial b-metric spaces and develops a framework for modelling multistage processes with several admissible terminal states. The contractive condition...

In the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more gener...

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets....

In this paper, we establish Hyers–Ulam–Rassias stability results belonging to two different set valued functional equations in several variables, namely additive and cubic. The results are obtained in the contexts of Banach spaces. The wo...

The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into va...

We present the concept of multivalued mappings in generalized modular metric spaces (GMMS). In addition, we give Caristi and Feng-Liu fixed point results for this type of mappings in GMMS. Then, we obtain an application for final outcomes in the sens...

After establishing some basic facts on binary relations and sequential convergences, we prove a relational modification of a false, but interesting lemma of Paweł Pasteczka on the constancy of the composition of certain set-valued functions [The...

In this work, we obtain a weak version of the turnpike property of trajectories of perturbed discrete disperse dynamical systems, which have a prototype in mathematical economics.

This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality of second-order for a set-valued fractional minimax problem. In addition, we define duals of the types Mond-Weir and Wolfe of second-order for the...

In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors’ problems of rational cont...

In this paper, we specified a method that generalizes a number of fixed point results for single and multi-valued mappings in the structure of extended b-metric spaces. Our results extend several existing ones including the results of Aleksic et al....

Hybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy $\mathfrak{Z}$-contraction in the...

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, ma...

Atanassov’s intuitionistic fuzzy sets extend the notion of fuzzy sets. In addition to Zadeh’s membership function, a non-membership function is also considered. Intuitionistic fuzzy values play a crucial role in both theoretical and pract...

Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given...

This paper introduces the concept of interval-valued T-spherical hesitant fuzzy set (IVTSHFS). Derived from the T-spherical fuzzy set, the IVTSHFS allows the membership, abstinence, and non-membership degrees of an element to be expressed as both int...

The interval-valued q-rung dual hesitant linguistic (IVq-RDHL) sets are widely used to express the evaluation information of decision makers (DMs) in the process of multi-attribute decision-making (MADM). However, the existing MADM method based on IV...

Global economic integration drives the development of dynamic competition. In a dynamic competitive environment, the ever-changing customer demands and technology directly affect the leadership of the core competence of enterprises. Therefore, assess...

This paper is devoted to investigating the existence of solutions for the fractional differential equation and fractional differential inclusion of order $\alpha \in (2,3]$ with affine periodic boundary value conditions. Applying the Leray–Scha...

In this article, we introduce the notion of approximate convexity for set-valued mappings, specifically in the forms of approximate pseudoconvexity and approximate quasiconvexity. These generalizations are motivated by the need to handle optimization...

In this article, we consider a Riemann–Liouville fractional-order nonlinear hybrid delay differential inclusion with a nonlinear set-valued nonlocal integral condition of fractional order. We prove some existence and uniqueness results in $C(I,\mathbb{R}$...

The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals that the idea has only been examined for crisp mappin...

The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we...

In this paper, we study the matrix representation of fuzzy soft sets, complement of fuzzy soft sets, product of fuzzy soft matrices and the application of fuzzy soft matrices in medical diagnosis presented by Lavanya and Akila. Additionally, a new me...

The metric average is a binary operation between sets in Rⁿ which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with pi...

This paper investigates a friction oscillator model in both its Integer-Order and Fractional-Order formulations. The lack of classical solutions for the governing differential equations with discontinuous right-hand sides is addressed by adopting a D...

We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the $RL$ integral, such as monotonicity, order continuity, bounded variation, convergence are obtain...

We provide some limit theorems for sequences of Riemann–Lebesgue integrable functions. More precisely, Lebesgue-type convergence and Fatou theorems are established. Then, these results are extended to the case of Riemann–Lebesgue integrable interval-...

In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then,...

Following the notions of $\mathrm{\Omega }$-set and $\mathrm{\Omega }$-algebra where $\mathrm{\Omega }$ is a complete lattice, we introduce P-algebras, replacing the lattice $\mathrm{\Omega }$ by a poset P. A P-algebra is a classical algebraic structure in which the usual equality is replaced...

For left and right λ-preinvex interval-valued functions (left and right λ-preinvex IVFs) in interval-valued Riemann operator settings, we create Hermite–Hadamard (H-H) type inequalities in the current study. Additionally, we creat...

The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved usi...

In this paper, we study a semilinear integro-differential inclusion in Banach spaces, under the action of infinitely many impulses. We provide the existence of mild solutions on a half-line by means of the so-called extension-with-memory technique, w...

In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. In...

In this paper, we consider optimization problems with stochastic constraints. We derive quantitative stability results for the optimal value function, the optimal solution set and the feasible solution set of optimization models in which the underlyi...

The connection between generalized convexity and symmetry has been studied by many authors in recent years. Due to this strong connection, generalized convexity and symmetry have arisen as a new topic in the subject of inequalities. In this paper, we...

In this paper, we deal with the properties and applications of a nonlinear scalarization function for sets by using the Minkowski difference. Under some suitable assumptions, the continuity and convexity concerned with the nonlinear scalarization fun...

The existence of two positive solutions for an elliptic differential inclusion is established, assuming that the nonlinear term is an upper semicontinuous set-valued mapping with compact convex values having subcritical growth. Our approach is based...