Fixed point property for digital spaces

被引：10

作者：

Han, Sang-Eon ^{[1
]}

机构：

[1] Chonbuk Natl Univ, Inst Pure & Appl Math, Dept Math Educ, Jeonju 561756, Jeonbuk, South Korea

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

Digital space; digitization; Khalimsky topology; Marcus-Wyse topology; fixed point property; digital homotopy almost fixed point property; almost fixed point property;

D O I：

10.22436/jnsa.010.05.20

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper compares the fixed point property (FPP for short) of a compact Euclidean plane with its digital versions associated with Khalimsky and Marcus-Wyse topology. More precisely, by using a Khalimsky and a Marcus-Wyse topological digitization, the paper studies digital versions of the FPP for Euclidean topological spaces. Besides, motivated by the digital homotopy fixed point property (DHFP for brevity) [O. Ege, I. Karaca, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029-1033], the present paper establishes the digital homotopy almost fixed point property (DHAFP for short) which is more generalized than the DHFP. Moreover, the present paper corrects some errors in [ O. Ege, I. Karaca, C. R. Math. Acad. Sci. Paris, 353 (2015), 1029-1033] and improves it. (C) 2017 All rights reserved.

引用

页码：2510 / 2523

页数：14

共 50 条

[41] Contractibility and fixed point property: the case of Khalimsky topological spaces
Han S.-E.
[J]. Fixed Point Theory and Applications, 2016 (1)
[42] On almost fixed point property of maps in topological vector spaces
Park, S
[J]. FIXED POINT THEORY AND APPLICATIONS, VOL 2, 2001, : 43 - 51
[43] ON THE FIXED POINT PROPERTY FOR NONEXPANSIVE MAPPINGS IN HYPERBOLIC GEODESIC SPACES
Piatek, Bozena
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2018, 19 (04) : 571 - 582
[44] SOME SPACES THAT DO NOT HAVE COMMON FIXED POINT PROPERTY
HUNEKE, JP
GLOVER, HH
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 29 (01) : 190 - &
[45] Spaces of compact operators on a Hilbert space with the fixed point property
Dowling, PN
Randrianantoanina, N
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 168 (01) : 111 - 120
[46] The fixed point property for subsets of some classical Banach spaces
Dowling, PN
Lennard, CJ
Turett, B
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 49 (01) : 141 - 145
[47] Fixed point theorems for the functions having monotone property or comparable property in the product spaces
Wu, Hsien-Chung
[J]. FIXED POINT THEORY AND APPLICATIONS, 2014,
[48] The fixed point property in Banach spaces via the strict convexity and the Kadec–Klee property
E. Hanebaly
[J]. Journal of Fixed Point Theory and Applications, 2020, 22
[49] Fixed point theorems for the functions having monotone property or comparable property in the product spaces
Hsien-Chung Wu
[J]. Fixed Point Theory and Applications, 2014
[50] THE KAKUTANI PROPERTY AND THE FIXED-POINT PROPERTY OF TOPOLOGICAL-SPACES WITH ABSTRACT CONVEXITY
WIECZOREK, A
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 168 (02) : 483 - 499

← 1 2 3 4 5 →