STRONG CONVERGENCE OF A NEW TWO-STEP ITERATIVE SCHEME FOR TWO QUASI-NONEXPANSIVE MULTI-VALUED MAPS IN BANACH SPACES

W. Cholamjiak; S. Suantai

STRONG CONVERGENCE OF A NEW TWO-STEP ITERATIVE SCHEME FOR TWO QUASI-NONEXPANSIVE MULTI-VALUED MAPS IN BANACH SPACES

Authors

W. Cholamjiak DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, CHIANG MAI UNIVERSITY, CHIANG MAI 50200, THAILAND
S. Suantai DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, CHIANG MAI UNIVERSITY, CHIANG MAI 50200, THAILAND

Keywords:

Quasi-nonexpansive multi-valued map, Nonexpansive multi-valued map, Common fixed point, Strong convergence, Banach space

Abstract

In this paper, a new two-step iterative scheme is introduced for two quasi-nonexpansivemulti-valued maps in Banach spaces. Strong convergence theorem of the purposed iterativescheme is established for quasi-nonexpansive multi-valued maps in Banach spaces. The resultobtained in this paper improve and extend the corresponding one announced by Shahzad andZegeye [N. Shahzad, H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valuedmaps in Banach spaces, Nonlinear Analysis 71 (2009) 838-844.].