Convergence of Ishikawa iterates of two mappings in modular function spaces

Authors

Afrah Ahmad Noan Abdou, King Abdulaziz University
Mohamed A. Khamsi, University of Texas at El Paso

Publication Date

3-25-2014

Document Type

Article

Comments

Abdou, A.A.N., Khamsi, M.A. & Khan, A.R. Fixed Point Theory Appl (2014) 2014: 74. https://doi.org/10.1186/1687-1812-2014-74

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.