SEMI-NORMAL STRUCTURE AND BEST PROXIMITY PAIR RESULTS IN CONVEX METRIC SPACES

被引：19

作者：

Gabeleh, Moosa ^{[1
]}

机构：

[1] Ayatollah Boroujerdi Univ, Dept Math, Boroujerd, Iran

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2014年 / 8卷 / 02期

关键词：

Best proximity pair; semi-normal structure; strongly noncyclic relatively C-nonexpansive; convex metric space; RELATIVELY NONEXPANSIVE-MAPPINGS; POINT THEOREM; ALGORITHM;

D O I：

10.15352/bjma/1396640065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new geometric notion on a nonempty and convex pair of subsets of a convex metric space X, called semi-normal structure, is introduced and used to investigate the existence of best proximity pairs for a new class of mappings, called strongly noncyclic relatively C-nonexpansive. We also study the structure of minimal sets of strongly noncyclic relatively C-nonexpansive mappings in the setting of convex metric spaces.

引用

页码：214 / 228

页数：15

共 17 条

[1]

Abkar A, 2013, J NONLINEAR CONVEX A, V14, P653

[2] Global Optimal Solutions of Noncyclic Mappings in Metric Spaces [J].

Abkar, A. ;

Gabeleh, M. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 153 (02) :298-305

[3] A GENERAL ITERATIVE ALGORITHM FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES [J].

Ali, Bashir ;

Ugwunnadi, Godwin C. ;

Shehu, Yekini .

ANNALS OF FUNCTIONAL ANALYSIS, 2011, 2 (02) :10-21

[4] ON THE SUZUKI NONEXPANSIVE-TYPE MAPPINGS [J].

Betiuk-Pilarska, Anna ;

Wisnicki, Andrzej .

ANNALS OF FUNCTIONAL ANALYSIS, 2013, 4 (02) :72-86

[5]

Brodskii M.S., 1948, Doki. Akad. Nauk. SSSR, V59, P837

[6]

Chatterjea S.K., 1972, C. R. Acad. Bulg. Sci, V25, P727, DOI [10.1501/Commua1_0000000548, DOI 10.1501/COMMUA1_0000000548]

[7] Proximal normal structure and relatively nonexpansive mappings [J].

Eldred, AA ;

Kirk, WA ;

Veeramani, P .

STUDIA MATHEMATICA, 2005, 171 (03) :283-293

[8] On the Structure of Minimal Sets of Relatively Nonexpansive Mappings [J].

Espinola, Rafa ;

Gabeleh, Moosa .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2013, 34 (08) :845-860

[9]

Gabeleh M., FIXED POINT IN PRESS

[10]

GOEBEL K, 1975, ANN U M CURIE SKLODO, V29, P73

← 1 2 →