×
Zhu, Jin-Hua; Chang, Shih-Sen

Halpern-Mann’s iterations for Bregman strongly nonexpansive mappings in reflexive Banach spaces with applications. (English) Zbl 1279.47091

J. Inequal. Appl. 2013, Paper No. 146, 14 p. (2013).
Summary: We investigate strong convergence for Bregman strongly nonexpansive mappings by modifying Halpern and Mann’s iterations in the framework of a reflexive Banach space. As applications, we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive Banach spaces.

Cited in 1 Review
Cited in 11 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

Bregman strongly nonexpansive mapping; Bregman projection; Legendre function; totally convex function; Halpern’s iteration; Mann’s iteration
Cite Review PDF
Full Text: DOI

References:

[1] doi:10.1090/S0002-9939-1953-0054846-3 · doi:10.1090/S0002-9939-1953-0054846-3
[2] doi:10.1090/S0002-9904-1967-11864-0 · Zbl 0177.19101 · doi:10.1090/S0002-9904-1967-11864-0
[3] doi:10.1007/BF01190119 · Zbl 0797.47036 · doi:10.1007/BF01190119
[4] doi:10.1090/S0002-9939-97-04033-1 · Zbl 0888.47034 · doi:10.1090/S0002-9939-97-04033-1
[5] doi:10.1017/S0004972700020116 · Zbl 1030.47036 · doi:10.1017/S0004972700020116
[6] doi:10.1016/j.jmaa.2005.05.023 · Zbl 1095.47034 · doi:10.1016/j.jmaa.2005.05.023
[7] doi:10.1016/j.na.2010.07.031 · Zbl 1234.47054 · doi:10.1016/j.na.2010.07.031
[8] doi:10.1137/S0363012902407120 · Zbl 1049.90053 · doi:10.1137/S0363012902407120
[9] doi:10.1137/070682071 · Zbl 1208.90133 · doi:10.1137/070682071
[10] doi:10.1016/j.na.2010.03.005 · Zbl 1226.47089 · doi:10.1016/j.na.2010.03.005
[11] doi:10.1142/S0219199701000524 · Zbl 1032.49025 · doi:10.1142/S0219199701000524
[12] doi:10.1007/BF00934676 · Zbl 0431.49042 · doi:10.1007/BF00934676
[13] doi:10.1080/02331939608844225 · Zbl 0883.47063 · doi:10.1080/02331939608844225
[14] doi:10.1137/070688717 · Zbl 1168.47047 · doi:10.1137/070688717
[15] doi:10.1017/S0004972700020116 · Zbl 1030.47036 · doi:10.1017/S0004972700020116
[16] doi:10.1007/s11228-008-0102-z · Zbl 1156.90426 · doi:10.1007/s11228-008-0102-z
[17] doi:10.1016/j.camwa.2011.12.026 · Zbl 1252.65100 · doi:10.1016/j.camwa.2011.12.026
[18] doi:10.1090/S0002-9947-1966-0192318-X · doi:10.1090/S0002-9947-1966-0192318-X
[19] doi:10.1080/01630560903499852 · Zbl 1200.47085 · doi:10.1080/01630560903499852
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.