Strong convergence of an inertial Halpern type algorithm in Banach spaces

In this article, we obtain the strong convergence of the new modified Halpern iteration process x(n+1) = alpha(n)u+(1-alpha(n))TnP(x(n) + theta(n)(x(n) - x(n-1))), n = 1,2,3, ... , to a common fixed point of {T-n}, where {T-n}(n=1)(infinity) is a family of nonexpansive mappings on the closed and convex subset C of a Banach space X, P : X -> C is a nonexpansive retraction, {alpha(n)} subset of [0, 1] and {theta(n)} subset of R+. Some applications of this result are also presented.