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Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures [PDF]
Mathematics, 2023 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 integrals,
Leifan Yan, Tong Kang, Huai Zhang
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Selection Properties and Set-Valued Young Integrals of Set-Valued Functions [PDF]
Results in Mathematics, 2020 AbstractThe paper deals with some selection properties of set-valued functions and different types of set-valued integrals of a Young type. Such integrals are considered for classes of Hölder continuous or with bounded Young p-variation set-valued functions.
Mariusz Michta, Jerzy Motyl
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Strong m-Convexity of Set-Valued Functions
Annales Mathematicae Silesianae, 2023 In this research we introduce the concept of strong m-convexity for set-valued functions defined on m-convex subsets of real linear normed spaces, a variety of properties and examples of these functions are shown, an inclusion of Jensen type is also ...
Lara Teodoro +3 more
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Set-Valued $$\alpha $$-Fractal Functions
Constructive Approximation, 2023 In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal functions. Further, we estimate the perturbation error between the given continuous function and its $\alpha$-fractal ...
Pandey, Megha +2 more
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On a Certain Generalized Functional Equation for Set-Valued Functions
Mathematics, 2020 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→cc(Y ...
Yaroslav Bazaykin +3 more
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Set-Valued T-Translative Functions and Their Applications in Finance
Mathematics, 2021 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 random
Andreas H. Hamel, Frank Heyde
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Spaces of Set-Valued Functions [PDF]
Transactions of the American Mathematical Society, 1972 If X X and Y
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Topologically Transitive and Mixing Properties of Set-Valued Dynamical Systems
Abstract and Applied Analysis, 2021 We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two properties for set-valued functions and generalize some results from a ...
Koon Sang Wong, Zabidin Salleh
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Contributions to the theory of set valued functions and set valued measures [PDF]
Transactions of the American Mathematical Society, 1987 Measurable multifunctions and multimeasures with values in a Banach space are studied. We start by proving a variation of the known Dunford theorem for weak compactness in
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Integration of compact set-valued functions [PDF]
Pacific Journal of Mathematics, 1975 provided by applying the McShane ^-integral. This integral is a Riemann-type integral and includes the Bochner, Lebesgue and other types of integrals, and by using Riemann sums it avoids deep measure theory. Thus, the ^-integral of set-valued functions contains other types of integrals such as the Hukuhara and Debreu integrals. Generalizations of known
Artstein, Zvi, Burns, John A.
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