Fixed Points of Nonlinear and Asymptotic Contractions in the Modular Space
نویسندگان
چکیده
The theory of modular space was initiated by Nakano [1] in connection with the theory of order spaces and was redefined and generalized byMusielak and Orlicz [2]. By defining a norm, particular Banach spaces of functions can be considered. Metric fixed theory for these Banach spaces of functions has been widely studied (see [3]). Another direction is based on considering and abstractly given functional which control the growth of the functions. Even though a metric is not defined, many problems in fixed point theory for nonexpansive mappings can be reformulated in modular spaces. In this paper, a fixed point theorem for nonlinear contraction in the modular space is proved. Moreover, Kirk’s fixed point theorem for asymptotic contraction is presented in this space. In order to do this and for the sake of convenience, some definitions and notations are recalled from [1–6].
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