Convergence of Ishikawa iterates of two mappings in modular function spaces

Abstract

We establish convergence in the modular sense of an iteration scheme associated with a pair of mappings on a nonlinear domain in modular function spaces. In particular, we prove that such a scheme converges to a common fixed point of the mappings. Our results are generalization of known similar results in the non-modular setting. In particular, we avoid smoothness of the norm in the case of Banach spaces and that of the triangle inequality of the distance in metric spaces. © 2014 Abdou et al.; licensee Springer.