On Fuzzy Modular Spaces
نویسندگان
چکیده
A modular space Xρ is defined by a corresponding modular ρ, that is,Xρ = {x ∈ X : ρ(λx) → 0 as λ → 0}. Based on definition of the modular space, Kozłowski [3, 4] introduced the notion ofmodular function space. In the sequel, Kozłowski and Lewicki [5] considered the problem of analytic extension of measurable functions in modular function spaces and discussed some extension properties by means of polynomial approximation. Afterwards, Kilmer and Kozłowski [6] studied the existence of best approximations in modular function spaces by elements of sublattices. In 1990, Khamsi et al. [7] initiated the study of fixed point theory for nonexpansive mappings defined on some subsets of modular function spaces. More researches on fixed point theory in modular function spaces can be found in [8–13]. In 2007, Nourouzi [14] proposed probabilistic modular spaces based on the theory of modular spaces and some researches on the Menger’s probabilistic metric spaces. A pair (X, ρ) is called a probabilistic modular space if X is a real vector space, ρ is a mapping from X into the set of all distribution functions (for x ∈ X, the distribution function ρ(x) is denoted by ρx, and ρx(t) is the value ρx at t ∈ R) satisfying the following conditions:
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ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013