In this article, we introduce an iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-asymptotically nonexpansive mappings, the set of the variational inequality for an a-inverse-strongly monotone operator, and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for...

where U : H1 → H1 and T : H2 → H2 are two firmly quasi-nonexpansive operators with nonempty fixed-point sets F(U) = {x ∈ H1 : Ux = x} and F(T ) = {x ∈ H2 : Tx = x}. Note that by taking H2 = H3 and B = I, we recover the split common fixed-point problem originally introduced in Censor and Segal (J. Convex Anal. 16:587-600, 2009). In this paper, we will continue to consider the split common fixed-...

1 School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China 2 Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea 3 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA 4 Mathematics and Statistics Department, King Fahd Univer...

and Applied Analysis 3 for all x, y ∈ C, where cn max{0, supx,y∈C ‖Tnx − Tny‖ − ‖x − y‖ } so that limn→∞cn 0. Hence, T is a generalized asymptotically nonexpansive mapping. The mapping T : C → C is said to be demiclosed at 0 if for each sequence {xn} in C converging weakly to x and {Txn} converging strongly to 0, we have Tx 0. A Banach space E is said to satisfy Opial’s property, see 4 , if for...

* Correspondence: czcheng@bjut. edu.cn College of Applied Science, Beijing University of Technology, Beijing 100124, PR China Full list of author information is available at the end of the article Abstract In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings {Ak}k=1 and a system of bifunctions {fk}k=1 satisfying c...

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...