Eur. Phys. J. Special Topics 226, 3667–3680 (2017)
https://doi.org/10.1140/epjst/e2018-00023-5

Regular Article

Iterated convergence on Banach space valued functions of abstract g-fractional calculus

¹ Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
² Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

^a e-mail: ganastss@memphis.edu

Received: 1 June 2017
Received in final form: 10 April 2018
Published online: 19 July 2018

Abstract

The novelty of this paper is the design of suitable iterative methods for generating a sequence approximating solutions of equations on Banach spaces. Applications of the semi-local convergence are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.