An iterative method for total quasi-phi-asymptotically nonexpansive semi-groups and generalized mixed equilibrium problems in Banach spaces

作者：Jeong Jae Ug^*; Kim Soo Hwan

来源：Applied Mathematics and Computation, 2015, 254: 39-48.

DOI：10.1016/j.amc.2014.12.135

• Total quasi-phi-asymptotically nonexpansive semi-group
• Quasi-phi-asymptotically nonexpansive semi-group
• Quasi-phi-nonexpansive semi-group
• Generalized mixed equilibrium problem

In this paper, we introduce an iterative scheme by the modified Halpern-Mann-type for total quasi-phi-asymptotically nonexpansive semi-groups and prove the strong convergence theorem using our new iterative process which converges strongly to a common element of the set of common fixed points for total quasi-phi-asymptotically nonexpansive semi-groups and the set of solutions of generalized mixed equilibrium problem in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property using the properties of the generalized f-projection operator. Our results extend and improve the corresponding recent results in the literature.

• 出版日期2015-3-1