Best proximity points of cyclic mappings

被引：69
作者：
Karapinar, Erdal [1 ]
机构：
[1] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey
来源：
APPLIED MATHEMATICS LETTERS | 2012年 / 25卷 / 11期
关键词：
Cyclic contraction; Best proximity points; Fixed point theory;
D O I：
10.1016/j.aml.2012.02.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this this manuscript, we proved that the existence of best proximity points for the cyclic operators T defined on a union of subsets A, B of a uniformly convex Banach space X with T (A) subset of B, T(B) subset of A and satisfying the condition parallel to Tx - Yy parallel to <= alpha/3[parallel to x-y parallel to + parallel to Tx - x parallel to + parallel to Ty - y parallel to] + (1 - alpha)diam(A, B) for alpha is an element of (0, 1) and for all x is an element of A, for all y is an element of B, where diam(A, B) = inf{parallel to x - y parallel to : x is an element of A, y is an element of B}. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1761 / 1766
页数：6
相关论文
共 11 条
[1]   Results on the Existence and Convergence of Best Proximity Points [J].
Abkar, Ali ;
Gabeleh, Moosa .
FIXED POINT THEORY AND APPLICATIONS, 2010,
[2]   Convergence and existence results for best proximity points [J].
Al-Thagafi, M. A. ;
Shahzad, Naseer .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (10) :3665-3671
[3]  
Albiac F, 2006, GRAD TEXTS MATH, V233, P1
[4]   Proximal pointwise contraction [J].
Anuradha, J. ;
Veeramani, P. .
TOPOLOGY AND ITS APPLICATIONS, 2009, 156 (18) :2942-2948
[5]  
Banach S., 1922, Fund. Math., V3, P133, DOI [10.4064/fm-3-1-133-181, DOI 10.4064/FM-3-1-133-181]
[6]   GENERALIZATION OF BANACHS CONTRACTION PRINCIPLE [J].
CIRIC, LB .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 45 (02) :267-273
[7]  
Derafshpour M, 2011, TOPOL METHOD NONL AN, V37, P193
[8]   Existence and convergence of best proximity points [J].
Eldred, A. Anthony ;
Veeramani, P. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (02) :1001-1006
[9]   Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps [J].
Karpagam, S. ;
Agrawal, Sushama .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (04) :1040-1046
[10]  
Kirk W.A., 2003, Fixed Point Theory, V4, P79
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