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Mathematics
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Set-Valued Analysis II
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Set-Valued Analysis II

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (20 October 2022) | Viewed by 9410

Special Issue Editors

Dr. Anca Croitoru

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Guest Editor
Faculty of Mathematics, University \"Alexandru Ioan Cuza\" of Iasi, Bd. Carol I, No. 11, 700506 Iasi, Romania
Interests: set-valued measures; set-valued integrals; non-additive measures; non-additive integrals; set-valued functions; almost linear spaces; approximate metrics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Radko Mesiar

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Guest Editor
Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry, Slovak University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia
Interests: aggregation operators and related operators; triangular norms; copulas; fuzzy sets and fuzzy logic; uncertainty modeling; measure theory; intelligent computing
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Anna Rita Sambucini

E-Mail Website
Guest Editor
Department of Mathematics and Computer Sciences, University of Perugia 1, Via Vanvitelli - 06123 Perugia, Italy
Interests: set-valued measures integrals; non-additive measures integrals; set-valued functions
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Bianca Satco

E-Mail Website
Guest Editor
Faculty of Electrical Engineering and Computer Science, “Stefan cel Mare” University of Suceava, Universitatii 13, Suceava, Romania
Interests: set-valued analysis (set-valued integrals in Banach spaces, differential and integral inclusions); measure differential equations and inclusions; bounded variation and regulated functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to publishing previously unpublished original papers with a high impact in all domains of set-valued analysis, both in theory and in applications. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, decision theory, game theory, nonlinear programming, biomathematics, or statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics that attracts an impressive number of researchers.

Prof. Dr. Anca Croitoru
Prof. Dr. Radko Mesiar
Prof. Dr. Anna Rita Sambucini
Prof. Dr. Bianca Satco
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • General set-valued functions 
  • Set-valued integrals 
  • Set-valued measures 
  • Analysis of differential inclusions 
  • Set-valued aggregation functions 
  • Inequalities in set-valued frame 
  • Convergence theorems in set-valued frame
  • Related topics in measure theory
  • Related topics

Published Papers (6 papers)

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Research

9 pages, 281 KiB  
Article
Convolution of Decomposition Integrals
by Adam Šeliga
Mathematics 2022, 10(5), 747; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050747 - 26 Feb 2022
Cited by 2 | Viewed by 926
Abstract
Four different types of convolutions of aggregation functions (the upper, the lower, the super-, and the sub-convolution) are examined in the setting of both sub- and super-decomposition integrals defined on a finite space. Examples of the results of the paper are provided. As [...] Read more.
Four different types of convolutions of aggregation functions (the upper, the lower, the super-, and the sub-convolution) are examined in the setting of both sub- and super-decomposition integrals defined on a finite space. Examples of the results of the paper are provided. As a by-product, the super-additive transformation of sub-decomposition integrals and the sub-additive transformation of super-decomposition integrals are fully characterized. Possible applications are indicated. Full article
(This article belongs to the Special Issue Set-Valued Analysis II)
32 pages, 428 KiB  
Article
Evolution Problems with m-Accretive Operators and Perturbations
by Charles Castaing, Christiane Godet-Thobie, Manuel D. P. Monteiro Marques and Anna Salvadori
Mathematics 2022, 10(3), 317; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030317 - 20 Jan 2022
Cited by 5 | Viewed by 1345
Abstract
This paper is devoted to the study of perturbation evolution problems involving time-dependent m-accretive operators. We present for a specific class of m-accretive operators with convex weakly compact-valued perturbation, some results about the existence of absolutely continuous solutions and BRVC solutions. [...] Read more.
This paper is devoted to the study of perturbation evolution problems involving time-dependent m-accretive operators. We present for a specific class of m-accretive operators with convex weakly compact-valued perturbation, some results about the existence of absolutely continuous solutions and BRVC solutions. We finish by giving several applications to various domains such as relaxation results, second-order evolution inclusions, fractional-order equations coupled with m-accretive operators and Skorohod differential inclusions. Full article
(This article belongs to the Special Issue Set-Valued Analysis II)
16 pages, 325 KiB  
Article
Solvability for a Class of Integro-Differential Inclusions Subject to Impulses on the Half-Line
by Paola Rubbioni
Mathematics 2022, 10(2), 224; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020224 - 12 Jan 2022
Cited by 2 | Viewed by 1137
Abstract
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, which consists of breaking down the problem [...] Read more.
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, which consists of breaking down the problem in an iterate sequence of non-impulsive Cauchy problems, each of them originated by a solution of the previous one. The key that allows us to employ this method is the definition of suitable auxiliary set-valued functions that imitate the original set-valued nonlinearity at any step of the problem’s iteration. As an example of application, we deduce the controllability of a population dynamics process with distributed delay and impulses. That is, we ensure the existence of a pair trajectory-control, meaning a possible evolution of a population and of a feedback control for a system that undergoes sudden changes caused by external forces and depends on its past with fading memory. Full article
(This article belongs to the Special Issue Set-Valued Analysis II)
11 pages, 276 KiB  
Article
Inverse Result of Approximation for the Max-Product Neural Network Operators of the Kantorovich Type and Their Saturation Order
by Marco Cantarini, Lucian Coroianu, Danilo Costarelli, Sorin G. Gal and Gianluca Vinti
Mathematics 2022, 10(1), 63; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010063 - 25 Dec 2021
Cited by 6 | Viewed by 2036
Abstract
In this paper, we consider the max-product neural network operators of the Kantorovich type based on certain linear combinations of sigmoidal and ReLU activation functions. In general, it is well-known that max-product type operators have applications in problems related to probability and fuzzy [...] Read more.
In this paper, we consider the max-product neural network operators of the Kantorovich type based on certain linear combinations of sigmoidal and ReLU activation functions. In general, it is well-known that max-product type operators have applications in problems related to probability and fuzzy theory, involving both real and interval/set valued functions. In particular, here we face inverse approximation problems for the above family of sub-linear operators. We first establish their saturation order for a certain class of functions; i.e., we show that if a continuous and non-decreasing function f can be approximated by a rate of convergence higher than 1/n, as n goes to +∞, then f must be a constant. Furthermore, we prove a local inverse theorem of approximation; i.e., assuming that f can be approximated with a rate of convergence of 1/n, then f turns out to be a Lipschitz continuous function. Full article
(This article belongs to the Special Issue Set-Valued Analysis II)
10 pages, 285 KiB  
Article
Four Types of Fixed-Point Theorems for Multifunctions in Probabilistic Metric Spaces
by Endre Pap
Mathematics 2021, 9(24), 3212; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243212 - 12 Dec 2021
Cited by 1 | Viewed by 1634
Abstract
An overview of fixed-point theorems (F.P.T.s) for multifunctions in probabilistic metric spaces is given. Extensions of the fixed-point theorems on probabilistic metric spaces of Nadler, Hadžić, Itoh, and Miheţ are presented. In the end, some hints about some further related investigations are given. [...] Read more.
An overview of fixed-point theorems (F.P.T.s) for multifunctions in probabilistic metric spaces is given. Extensions of the fixed-point theorems on probabilistic metric spaces of Nadler, Hadžić, Itoh, and Miheţ are presented. In the end, some hints about some further related investigations are given. Full article
(This article belongs to the Special Issue Set-Valued Analysis II)
15 pages, 301 KiB  
Article
Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
by Radko Mesiar and Reza Saadati
Mathematics 2021, 9(14), 1602; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141602 - 07 Jul 2021
Cited by 2 | Viewed by 1288
Abstract
We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an approximation [...] Read more.
We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an approximation for a pseudo functional equation is called random HUR stability. We use a fixed point technique derived from the alternative fixed point theorem (FPT) to investigate random HUR stability of the Riemann–Liouville fractional equations in MB-spaces. As an application, we introduce a class of random Wright control function and investigate existence–uniqueness and Wright stability of these equations in MB-spaces. Full article
(This article belongs to the Special Issue Set-Valued Analysis II)
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