Strong convergence theorems of the Halpern-Mann’s mixed iteration for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping in Banach spaces
نویسندگان
چکیده
In this paper, we introduce a class of totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping to modify the Halpern-Mann-type iteration algorithm for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping, which has the strong convergence under a limit condition only in the framework of Banach spaces. Our results are applied to study the approximation problem of solution to a system of equilibrium problems. Also, the results presented in the paper improve and extend the corresponding results of Chang et al. (Appl. Math. Comput. 218:7864-7870, 2012) and others.
منابع مشابه
Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications
In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly co...
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