Strong convergence theorem for solving split equality fixed point problem which does not involve the prior knowledge of operator norms

‎Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space‎. ‎So many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎but as widely known the computation of these algorithms may be difficult and for this reason‎, ‎some researchers have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm‎. ‎To the best of our knowledge most of the works in literature that do not involve the calculation or estimation of the operator norm only obtained weak convergence results‎. ‎In this paper, by appropriately modifying the simultaneous iterative algorithm introduced by Zhao‎, ‎we state and prove a strong convergence result for solving split equality problem‎. ‎We present some applications of our result and then give some numerical example to study its efficiency and implementation at the end of the paper‎.