Abstract
Kirk and Xu studied the existence of fixed points of asymptotic pointwise nonexpansive mappings in the Banach space. In this paper, we investigate these kinds of mappings in modular spaces. Moreover, we prove the existence of fixed points of asymptotic pointwise nonexpansive mappings in modular spaces. The results improve and extend the corresponding results of Kirk and Xu (2008) to modular spaces.
Highlights
The theory of modular spaces was initiated by Nakano 1 in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz 2 in 1959
Kirk and Xu studied the existence of fixed points of asymptotic pointwise nonexpansive mappings in the Banach space
Kuaket and Kumam 5 proved the existence of fixed points of asymptotic pointwise contractions in modular spaces
Summary
The theory of modular spaces was initiated by Nakano 1 in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz 2 in 1959. Kirk and Xu studied the existence of fixed points of asymptotic pointwise nonexpansive mappings in the Banach space. We prove the existence of fixed points of asymptotic pointwise nonexpansive mappings in modular spaces.
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