An explicit midpoint algorithm in Banach spaces

A generalized explicit midpoint algorithm for quasi-nonexpansive mappings in Banach spaces is introduced. The main convergence result extends a recent previous one, G. Marino, B. Scardamaglia, R. Zaccone, A general viscosity explicit midpoint rule for quasi-nonexpansive mappings, J. Nonlinear and Convex Analysis, to a more general setting of Banach spaces. Examples of the obtained results, in lp and Lp spaces, are included. The starting point is the classical Explicit Midpoint Rule (EMR) for constructing polygonals approximating a solution of an ordinary differential equation.