Strong convergence result for split inclusion problems in Banach spaces

By using Halpern’s type iteration process, an iterative algorithm is proposed to study the split inclusion problem and fixed points of a relatively nonexpansive mapping in Banach spaces. This method uses dynamic stepsize that is generated at each iteration by simple computations, which allows it to be easily implemented without the prior information of the operator norm. Then, the main result is used to study the fixed points of a countable family of relatively nonexpansive mappings and the semigroup of relatively nonexpansive mappings. Finally, a numerical example is provided to illustrate the main result.

کلیدواژه ها:

split feasibility problem ، Uniformly convexity ، Uniformly smoothness ، fixed point problem