ABSOLUTE DERIVATIVE OF SET-VALUED MAPS

被引：0

作者：

Muslikh, Mohamad ^{[1
]}

Kilicman, Adem ^{[2
]}

机构：

[1] Univ Brawijaya, Fac Math & Sci, Dept Math, Malang 65143, East Java, Indonesia

[2] Univ Putra malaysia, Fac Sci, Dept Math, Serdang, Selangor, Malaysia

来源：

BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 14卷 / 03期

关键词：

Set-valued; Defferentiation; INTERVAL; DIFFERENTIABILITY; CALCULUS;

D O I：

10.54671/BMAA-2022-3-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this article is to develop a differential calculus for set-valued functions with values in metric spaces of the family of all compact and convex subsets. Using only the metric Hausdorff on metric spaces and without using the Hukuhara difference, a concept of the derivative is introduced for set-valued functions in such metric spaces. The comparison with the other de-rivative definitions of the set-valued functions and the relation to the Lipschitz conditions was also investigated in this paper.

引用

页码：20 / 35

页数：16

共 50 条

[21] Convexity Criteria for Set-Valued Maps
Pham Huu Sach
Nguyen Dong Yen
[J]. Set-Valued Analysis, 1997, 5 (1): : 37 - 45
[22] Invariant measures of set-valued maps
Artstein, Z
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 252 (02) : 696 - 709
[23] NASH EQUILIBRIUM FOR SET-VALUED MAPS
GUILLERME, J
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 187 (03) : 705 - 715
[24] APPROXIMATION OF NONCONVEX SET-VALUED MAPS
BENELMECHAIEKH, H
DEGUIRE, P
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1991, 312 (05): : 379 - 384
[25] AN INVERSION THEOREM FOR SET-VALUED MAPS
AZE, D
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1988, 37 (03) : 411 - 414
[26] Set-valued maps for image segmentation
Lorenz, Thomas
[J]. Computing and Visualization in Science, 2001, 4 (01) : 41 - 57
[27] Convexity criteria for set-valued maps
Sach, PH
Yen, ND
[J]. SET-VALUED ANALYSIS, 1997, 5 (01): : 37 - 45
[28] TOPOLOGICAL ENTROPY FOR SET-VALUED MAPS
Carrasco-Olivera, Dante
Metzger Alvan, Roger
Morales Rojas, Carlos Arnoldo
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (10): : 3461 - 3474
[29] Invariant measures for set-valued maps
Gorbachev, A. N.
Stepin, A. M.
[J]. RUSSIAN MATHEMATICAL SURVEYS, 2009, 64 (06) : 1136 - 1138
[30] A SEQUENTIAL PROPERTY OF SET-VALUED MAPS
CASCALES, B
ORIHUELA, J
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 156 (01) : 86 - 100

← 1 2 3 4 5 →