Iterative methods for fixed point problems and generalized split feasibility problems in Banach spaces

In this paper, we study the Halpern type iterative algorithm to approximate a common solution of fixed point problems of an infinite In this paper, we study the Halpern type iterative algorithm to approximate a common solution of fixed point problems of an infinite family of demimetric mappings and generalized split feasibility problems with firmly nonexpansive-like mappings in Banach spaces. We also prove strong convergence theorems for a common solution of the above-said problems by the proposed iterative algorithm and discuss some applications of our results. The methods in this paper are novel and different from those given in many other paper. And the results are the extension and improvement of the recent results in the literature.