Article
Mathematics, Applied
Jae Hyoung Lee, Tien-Son Pham
Summary: In this paper, properties of semialgebraic set-valued maps with closed graphs are studied, including the equivalence between open mapping and locally closed range. Through Robinson's normal map formulation, results in the context of semialgebraic variational inequalities are derived. The study also shows the equivalence between openness and nonextremality for continuous single-valued maps from Rn to R.
SIAM JOURNAL ON OPTIMIZATION
(2022)
Article
Multidisciplinary Sciences
Mohammed Shehu Shagari, Trad Alotaibi, Rehana Tabassum, Awad A. Bakery, O. M. Kalthum S. K. Mohamed, Arafa O. Mustafa
Summary: The applications of non-zero self distance function have been recently discovered in both symmetric and asymmetric spaces. Only the idea of invariant points for crisp mappings in either symmetric or asymmetric spaces has been examined in the available literature. This paper aims to introduce the notion of invariant points for non-crisp set-valued mappings in metric-like spaces. The technique of ?-contraction and Feng-Liu's approach are combined to establish new versions of intuitionistic fuzzy functional equations, and fixed point theorems are studied without using the conventional Pompeiu-Hausdorff metric.
Article
Operations Research & Management Science
Tran Ngoc Tam
Summary: This paper introduces the concepts of strong t-quasiconvexity and strong t-quasiconvex-likeness, as well as relaxed Holder continuity, with respect to an ordering cone of a set-valued map. These concepts are then used to establish sufficient conditions for the non-emptiness of solution sets and the stability, in terms of Holder continuity, of solution maps to parametric set-valued Ky Fan inequalities. The approach presented in this paper is different from existing ones. Furthermore, an application of the main results to set-valued Nash equilibrium in games is also provided.
Article
Mathematics
Mohammed Shehu Shagari, Maha Noorwali, Akbar Azam
Summary: A new concept called b-hybrid fuzzy soft contraction in b-metric space is proposed in this study, and new criteria for the existence of fixed points for such mappings are investigated. The significance of the obtained principal result lies in the ability to specialize the contractive inequalities in various ways, depending on the choice of parameters, thereby unifying, deducing, and refining several corresponding results. Two applications regarding decision-making problems and an existence theorem of integral inclusion using fuzzy soft set-valued maps are considered to motivate further studies.
Article
Mathematics, Applied
Maysaa Al-Qurashi, Mohammed Shehu Shagari, Saima Rashid, Y. S. Hamed, Mohamed S. Mohamed
Summary: In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of b-metric spaces are examined. The concept of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps is introduced. Novel sufficient criteria for existence of solutions to an integral inclusion are investigated.
Article
Mathematics, Applied
Kendry J. Vivas, Victor F. Sirvent
Summary: In this article, we introduce a notion of metric entropy for an invariant measure associated with a set-valued map on a compact metric space. We describe its main properties and prove the Half Variational Principle, which establishes the relationship between metric entropy and the notion of topological entropy for this class of maps as given in [13].
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Applied
Eliza Jablonska, Wojciech Jablonski
Summary: This paper studies the fundamental properties of K-additive set-valued maps. Among other things, it is proven that K-lower (or weakly K-upper) boundedness on a large set implies K-continuity on the domain, and K-continuity implies K-homogeneity. The algebraic structure of the K-homogeneity set for K-additive set-valued maps is also examined.
RESULTS IN MATHEMATICS
(2023)
Article
Mathematics
Megha Pandey, Tanmoy Som, Saurabh Verma
Summary: In this paper, the concept of a-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers is introduced. The properties of such fractal functions are studied, and the perturbation error between the given continuous function and its a-fractal function is estimated. A new graph of a set-valued function that differs from the standard graph in the literature is defined, and bounds on the fractal dimension of this newly defined graph for special classes of set-valued functions are established. Additionally, the necessity of defining this new graph is explained through examples. Finally, it is proven that the new graph of an a-fractal function is an attractor of an iterated function system.
CONSTRUCTIVE APPROXIMATION
(2023)
Article
Computer Science, Theory & Methods
Jun Li
Summary: This note points out the invalidity of a theorem and the defects in two proofs in a paper, and raises an open problem regarding the characteristics of monotone measures.
FUZZY SETS AND SYSTEMS
(2022)
Article
Operations Research & Management Science
E. Hernandez, R. Lopez
Summary: This paper investigates the properties of Epi-convergence and compares it with other convergence notions used to study the stability of set optimization problems.
Article
Mathematics, Applied
M. Ivanov, M. Quincampoix, N. Zlateva
Summary: This paper presents a new derivative criterion for metric regularity of set-valued maps from a Frechet-Montel space to a Frechet space. Previous studies on such criteria have mainly focused on Banach spaces, but our work extends the research based on the Nash-Moser-Ekeland approach. As a result of our criterion, an implicit mapping result is also provided in this paper.
SET-VALUED AND VARIATIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Volker Branding
Summary: This article introduces a natural extension of the equation for harmonic maps between Riemannian manifolds, considering the impact of connections with non-vanishing torsion on the maps. The study presents new challenges in the field of harmonic maps equations.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics
Nira Dyn, Elza Farkhi, Alona Mokhov
Summary: We introduce the concept of metric divided differences for set-valued functions, which allows us to obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions using high-degree metric piecewise-polynomial interpolants. Additionally, we derive high-order approximations of set-valued functions using local metric approximation operators that reproduce high-degree polynomials.
CONSTRUCTIVE APPROXIMATION
(2023)
Article
Mathematics, Applied
Yiran He, Wending Xu
Summary: This paper examines perturbation analysis of metric regularity, establishing an improved stability result under Lipschitz set-valued perturbations, with more relaxed conditions and a more concise proof compared to existing results.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Monairah Alansari, Mohammed Shehu Shagari
Summary: This study introduces the idea of Presic-type intuitionistic fuzzy stationary point results within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed to complement their corresponding concepts related to multi-valued and single-valued mappings. Various consequences of our results in different types of mappings are emphasized and discussed.
