Abstract. Very recently, Moudafi proposed the following new convex feasibility problem in [10,11]: f ind x ∈ C, y ∈ Q such that Ax = By, where the two closed convex sets C and Q are the fixed point sets of two firmly quasi-nonexpansive mappings respectively, H 1 , H 2 and H 3 are real Hilbert spaces, A : H 1 → H 3 and B : H 2 → H 3 are two bounded linear operators. However, they just obtained weak convergence for such new split feasibility problem. In this paper, we introduce a new algorithm which is more general than the SIM-FPP algorithm presented by Moudafi in [11] and obtain strong and weak convergence theorems for the new split feasibility problem. Our results extend and improve the corresponding result of Moudafi [11].
Mathematics Subject Classifications: 47H09, 47J25
The purpose of this paper is to propose an algorithm for solving the split equality fixed point problem of asymptotically nonexpansive mappings in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems of the iterative scheme proposed in this paper are obtained.
In this paper, we establish new strong convergence theorems of proposed algorithms under suitable new conditions for the generalized split feasibility problem in Banach spaces. As applications, new strong convergence theorems for equilibrium problems, fixed point problems and split common fixed point problems are also studied. Our new results are distinct from recent results on the topic in the literature.
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