ASYMPTOTIC POINTWISE CONTRACTIONS IN MODULAR METRIC SPACES

Abstract

Kirk and Xu introduced the concept of asymptotic pointwise contractions and proved the existence of a xed point of asymptotic pointwise contractions in Banach space. V. V. Chistyakov proposed the concept of modular metric spaces. In this paper, the existence of fixed points for asymptotic pointwise contractions is studied in modular metric spaces. Moreover, the fixed point theorem for asymptotic pointwise nonexpansive mappings in modular metric spaces is also studied. The results improve and extend the results of Kirk and Xu [W. A. Kirk, Hongkun Xu, Asymptotic pointwise contractions, Nonlinear Anal., 69(2008)4706-4712] to modular metric spaces.