Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings

作者：Ceng Lu Chuan; Guu Sy Ming^*; Hu H Y; Yao Jen Chih

来源：Computers & Mathematics with Applications, 2011, 61(9): 2468-2479.

DOI：10.1016/j.camwa.2011.02.028

• Generalized equilibrium problem
• Relatively nonexpansive mapping
• Maximal monotone operator
• Hybrid shrinking projection method
• Strong convergence
• Uniformly smooth and uniformly convex Banach space

The purpose of this paper is to introduce and consider a hybrid shrinking projection method for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set boolean AND(infinity)(n=0) F(S(n)) of common fixed points of a countable family of relatively nonexpansive mappings {S(n)}(n=0)(infinity) and the set T(-1)0 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. It is proven that under appropriate conditions, the sequence generated by the hybrid shrinking projection method, converges strongly to some point in EP boolean AND T(-1)0 boolean AND (boolean AND(infinity)(n=0) F(S(n))). This new result represents the improvement, complement and development of the previously known ones in the literature.

• 出版日期2011-5
• 单位上海师范大学; 上海大学