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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2009; 46(3): 561-576

Printed May 1, 2009

https://doi.org/10.4134/JKMS.2009.46.3.561

Copyright © The Korean Mathematical Society.

Weak and strong convergence theorems for an asymptotically $k$-strict pseudo-contraction and a mixed equilibrium problem

Yonghong Yao, Haiyun Zhou, and Yeong-Cheng Liou

Tianjin Polytechnic University, Shijiazhuang Mechanical Engineering College, and Cheng Shiu University

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We introduce two iterative algorithms for finding a common element of the set of fixed points of an asymptotically $k$-strict pseudo-contraction and the set of solutions of a mixed equilibrium problem in a Hilbert space. We obtain some weak and strong convergence theorems by using the proposed iterative algorithms. Our results extend and improve the corresponding results of Tada and Takahashi [16] and Kim and Xu [8, 9].

Keywords: mixed equilibrium problems, fixed point problems, iterative algorithm, asymptotically $k$-strict pseudo-contraction, Hilbert space

MSC numbers: 49J30, 47H10, 47H17, 49M05, 90C25, 90C99

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