Algorithm for Two Generalized Nonexpansive Mappings in Uniformly Convex Spaces

被引：5

作者：

Usurelu, Gabriela Ioana ^{[1
]}

Turcanu, Teodor ^{[1
]}

Postolache, Mihai ^{[1
,2
,3
]}

机构：

[1] Univ Politehn Bucuresti, Dept Math & Informat, Bucharest 060042, Romania

[2] Romanian Acad, Gheorghe Mihoc Caius Iacob Inst Math Stat & Appl, Bucharest 050711, Romania

[3] Sichuan Univ, Business Sch, Chengdu 610064, Peoples R China

来源：

MATHEMATICS | 2022年 / 10卷 / 03期

关键词：

Garcia-Falset mapping; condition (E); Suzuki mapping; condition (C); beta)-generalized hybrid mappings; common fixed point; iteration; FIXED-POINT THEOREMS; WEAK-CONVERGENCE THEOREMS; NONLINEAR MAPPINGS; ITERATION SCHEME; OPERATORS;

D O I：

10.3390/math10030318

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the common fixed-point problem for a pair of Garcia-Falset mapping and (alpha,beta)-generalized hybrid mapping in uniformly convex Banach spaces. For this purpose, we construct a modified three-step iteration by properly including together these two types of mappings into its formula. Under this modified iteration, a necessary and sufficient condition for the existence of a common fixed point as well as weak and strong convergence outcomes are phrased under some additional conditions.

引用

页数：18

共 33 条

[21] On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval [J].

Phuengrattana, Withun ;

Suantai, Suthep .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (09) :3006-3014

[22] Approximating fixed points of generalized -nonexpansive mappings in Banach spaces by new faster iteration process [J].

Piri, H. ;

Daraby, B. ;

Rahrovi, S. ;

Ghasemi, M. .

NUMERICAL ALGORITHMS, 2019, 81 (03) :1129-1148

[23] A new iteration technique for nonlinear operators as concerns convex programming and feasibility problems [J].

Sahu, D. R. ;

Pitea, A. ;

Verma, M. .

NUMERICAL ALGORITHMS, 2020, 83 (02) :421-449

[24] WEAK AND STRONG-CONVERGENCE TO FIXED-POINTS OF ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS [J].

SCHU, J .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1991, 43 (01) :153-159

[25] APPROXIMATING FIXED-POINTS OF NONEXPANSIVE MAPPINGS [J].

SENTER, HF ;

DOTSON, WG .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (02) :375-380

[26] On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis [J].

Sintunavarat, Wutiphol ;

Pitea, Ariana .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (05) :2553-2562

[27] Fixed point theorems and convergence theorems for some generalized nonexpansive mappings [J].

Suzuki, Tomonari .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 340 (02) :1088-1095

[28] Weak convergence theorems for nonexpansive mappings and monotone mappings [J].

Takahashi, W ;

Toyoda, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2003, 118 (02) :417-428

[29]

Takahashi W, 2010, J NONLINEAR CONVEX A, V11, P79

[30] A New Iteration Scheme For Approximating Fixed Points of Nonexpansive Mappings [J].

Thakur, Balwant Singh ;

Thakur, Dipti ;

Postolache, Mihai .

FILOMAT, 2016, 30 (10) :2711-2720

← 1 2 3 4 →