SOLVING SPLIT FEASIBILITY PROBLEMS AND FIXED POINT PROBLEMS USING EXTRAGRADIENT METHOD IN BANACH SPACES

In this paper, we propose a new extragradient algo- rithm for finding a common element of the fixed points set of a infinite family of relatively nonexpansive mappings and the set of solutions of a split feasibility problem in Banach spaces. We prove strong convergence theorem by this method under suitable con- ditions. Using FMINCON optimization toolbox in MATLAB, we give a numerical example to demonstrate the usability of our result.