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 spaceý. ýSo many have used algorithms involving the operator norm for solving split equality fixed point problemý, ýbut as widely known the computation of these algorithms may be difficult and for this reasoný, ýsome 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 normý. ýTo 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 resultsý. ýIn this paper, by appropriately modifying the simultaneous iterative algorithm introduced by Zhaoý, ýwe state and prove a strong convergence result for solving split equality problemý. ýWe present some applications of our result and then give some numerical example to study its efficiency and implementation at the end of the paperý.