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new inertial iterative algorithm for approximating solution of split equality fixed point problem (SEFPP) for quasi-ϕ-nonexpansive mappings is introduced and studied in p-uniformly convex and uniformly smooth real Banach spaces, p > 1. A strong convergence theorem is proved without imposing any compactness-type condition on the mappings. Our theorems complement several important recent results that have been proved in 2-uniformly convex and uniformly smooth real Banach spaces. It is well known that these spaces do not include Lp, lp and the Sobolev spaces Wmp(Ω), for 2 < p < ∞. Our theorems, in particular, are applicable in these spaces. Furthermore, application of our theorem to split equality variational inclusion problem is presented. Finally, numerical examples are presented to illustrate the convergence of our algorithms. [ABSTRACT FROM AUTHOR]