Krasnoselski-Mann iterative method for finding a common solution of hierarchical fixed point problems and split mixed equilibrium problems

In this talk, we introduce a modified Krasnoselski-Mann type iterative method for finding a common solution of a split mixed equilibrium problem and a hierarchical fixed point problem of a finite family of $k$-strictly pseudocontractive non-self mappings. Many of the algorithms for solving the split mixed equilibrium problem involves step size which depends on the norm of a bounded linear operator. Since the computation of the operator norm is very difficult, we formulate our iterative algorithm in such a way that the implementation of the proposed algorithm does not require any prior knowledge of operator norm. Weak convergence results are established under mild conditions. We also establish strong convergence results for a certain class of hierarchical fixed point and split equilibrium problem.