Modular spaces

On a class of nonlinear problems involving a p(x)-Laplace type operator

“…Variable exponent Lebesgue spaces appeared for the first time in literature as early as 1931 in an article by W. Orlicz [23]. The spaces L p(x) are special cases of Orlicz spaces L ϕ originated by Nakano [22] and developed by Musielak and Orlicz [20], [21], where f ∈ L ϕ if and only if ϕ(x, |f (x)|) dx < ∞ for a suitable ϕ. Variable exponent Lebesgue spaces on the real line have been independently developed by Russian researchers.…”

Fixed Point Theory For Generalized Quasi-contraction Maps In Modular Metric Spaces

“…The theory of modular spaces was initiated by Nakano in 1950 [12], and generalized and redefined by Musielak and Orlicz [ [10], [11]] in 1959. In 2008, Chistyakov [7] introduced the notation of modular metric spaces generated by Fmodular and develop the theory of modular spaces, by the same idea he was   , possibly depending on (1)  is non-decreasing;…”

Existence Results for the p(x)-Laplacian with Nonlinear Boundary Condition

“…Variable exponent Lebesgue spaces appeared for the first time in the literature as early as 1931 in an article by Orlicz 4 . The spaces L p x are special cases of Orlicz spaces L ϕ originated by Nakano 5 and developed by Musielak and Orlicz 6,7 , where f ∈ L ϕ if and only if ϕ x, |f x | dx < ∞ for a suitable ϕ. Variable exponent Lebesgue spaces on the real line have been independently developed by Russian researchers.…”