An abstract point of view on iterative approximation schemes of fixed points for multivalued operators

被引：16

作者：

Petrusel, Adrian ^{[1
]}

Rus, Ioan A. ^{[1
]}

机构：

[1] Univ Babes Bolyai, Dept Math, Cluj Napoca 400084, Romania

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2013年 / 6卷 / 02期

关键词：

multivalued operator; fixed point; strict fixed point; iterative scheme; multivalued Picard operator; multivalued weakly Picard operator; ISHIKAWA ITERATION; DATA DEPENDENCE; MAPPINGS; MANN; SET;

D O I：

10.22436/jnsa.006.02.05

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems are also presented.

引用

页码：97 / 107

页数：11

共 53 条

[1] Andres J., 2003, Topological Fixed Point Theory and Its Applications, V1
[2] [Anonymous], 2003, FIXED POINT THEOR-RO
[3] [Anonymous], 2004, P IC FIX POINT THEOR
[4] [Anonymous], 1953, Theory and Applications of Distance Geometry
[5] Aubin J.P., 1984, DIFFERENTIAL INCLUSI
[6] Berinde V, 2007, LECT NOTES MATH, V1912, P1
[7] Carl S, 2011, FIXED POINT THEORY IN ORDERED SETS AND APPLICATIONS: FROM DIFFERENTIAL AND INTEGRAL EQUATIONS TO GAME THEORY, P1, DOI 10.1007/978-1-4419-7585-0
[8] Iteration processes for approximating fixed points of operators of monotone type
Chang, SS
Tan, KK
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1998, 57 (03) : 433 - 445
[9] Chidume C., 2009, GEOMETRIC PROPERTIES
[10] MULTI-VALUED CONTRACTION MAPPINGS IN GENERALIZED METRIC SPACES
COVITZ, H
NADLER, SB
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1970, 8 (01) : 5 - &

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