| The equilibrium problem and the split feasibility problem are two hot issues in the field of nonlinear analysis recently; it provides us with a unified framework for studying a wide class of problems arising in finance transportation, structural analysis, elasticity, game theory and optimization. So there is important academic significance and application value in the research of nonlinear analysis. In resent years, many scholars have considered a lot of iterative algorithms about equilibrium problems and many significant research results have been achieved. And the split feasibility problem has a very strong application setting. For example, CT in the medical field; smart antenna in military field; electronic warning; image processing technology; language processing system; and HD digtal TV technology. In particular, it play a important role in signal processing and image restoration. We usually research the technical issues in the frame of the split feasibility problems. So establish effective iterative algorithms to approach its solution become one of the most popular subjects. The split fixed point problem is a important branch of the split feasibility problem, which makes the split fixed point problem get maximum solicitude. In resent years, many scholars have considered a lot of iterative algorithms about equilibrium problems and the split fixed point problem and many significant research results have been achieved.Inspired and motivated by these research results, in this paper we mainly study the following three problems:Firstly, we construct a hybrid algorithm to find a common element of set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a countable family of quasi-(p-asymptotically nonexpansive multi-valued mappings in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. Meanwhile we get a strong convergent theorem. The results extend the related results announced by Shisheng Chang (2009), Jinfang Tang (2010) and Homaeipour, Razani (2011)Secondly, we introduce a viscosity approximation method for solving the split common fixed-point problem for the class of demicontractive mappings in Hilbert spaces. The results extend and improve the corresponding results announced by Moudafi (2011) Jin Zhao and Songnian He(2012).Lastly, we construct a iterative algorithm for solving the split common fixed-point problem for the class of quasi-total asymptotically strictly pseudocontractive mappings in Hilbert spaces. And we also get a strong and weak convergence theorem. The results improve and extend the corresponding results announced by Moudafi (2011), L. J. Qin, L. Wang (2012) and Jing Na, Lin Wang, and Zhaoli Ma (2012)... |
