A Modified Krasnosel'skii-Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

被引：10

作者：

Berinde, Vasile ^{[1
,2
]}

机构：

[1] Tech Univ Cluj Napoca, North Univ Ctr Baia Mare, Dept Math & Comp Sci, Victoriei Str 76, Baia Mare 430122, Romania

[2] Acad Romanian Sci, Ilfov Str 3, Bucharest 050045, Romania

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 01期

关键词：

Hilbert space; enriched nonexpansive mapping; fixed point; modified Krasnosel'skii-Mann algorithm; strong convergence; STRONG-CONVERGENCE THEOREMS; NONLINEAR MAPPINGS; CONSTRUCTION;

D O I：

10.3390/sym14010123

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel'skii-Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel'skii-Mann algorithm and of the simple Krasnosel'skii fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel'skii fixed point algorithm than with the modified Krasnosel'skii-Mann algorithm.

引用

页数：12

共 25 条

[1] Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming
Abbas, Mujahid
Anjum, Rizwan
Berinde, Vasile
[J]. SYMMETRY-BASEL, 2021, 13 (08):
[2] Agarwal RP, 2009, TOPOL FIXED POINT TH, V6, P1, DOI 10.1007/978-0-387-75818-3_1
[3] Bagherboum M, 2014, B IRAN MATH SOC, V40, P823
[4] Berinde V, 2007, LECT NOTES MATH, V1912, P1
[5] Berinde V, 2020, CARPATHIAN J MATH, V36, P27
[6] Berinde V, 2019, CARPATHIAN J MATH, V35, P293
[7] SEMICONTRACTIVE AND SEMIACCRETIVE NONLINEAR MAPPINGS IN BANACH SPACES
BROWDER, FE
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (04) : 660 - &
[8] CONSTRUCTION OF FIXED POINTS OF NONLINEAR MAPPINGS IN HILBERT SPACE
BROWDER, FE
PETRYSHY.WV
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1967, 20 (02) : 197 - &
[9] Chidume C, 2009, LECT NOTES MATH, V1965, P1
[10] Goebel K., 1984, Uniform convexity, hyperbolic geometry, and nonexpansive mappings

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