A new concept of smoothness in Orlicz spaces

In a 2015 article Cuenya and Ferreyra defined a class of functions in Lp-spaces, denoted by cpn(x). The class cpn(x) contains the class of Lp -differentiability functions, denoted by tpn(x), introduced in a 1961 article by Calderón-Zygmun. A more recent paper by Acinas, Favier and Zó introduced a new class of functions in Orlicz spaces LΦ, called L Φ-differentiable functions in the present article. The class of LΦ-differentiable functions is closely related to the class tpn(x). In this work, we define a class of functions in LΦ, denoted by cΦn(x). The class cΦn(x) is more general than the class of LΦ-differentiable functions. We prove the existence of the best local Φ-approximation for functions in cΦn(x) and study the convexity of the set of cluster points of the set of best Φ-approximations to a function on an interval when their measures tend to zero.Fil: Ferreyra, David Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; ArgentinaFil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Roldán, Marina Vanesa. Universidad Nacional de La Pampa. Facultad de Ingeniería; Argentin