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