摘要 : In a 2015 article Cuenya and Ferreyra defined a class of functions in L-p-spaces, denoted by c(n)(p)(x). The class c(n)(p)(x) contains the class of L-p-differentiability functions, denoted by t(n)(p)(x), introduced in a 1961 artic... 展开 In a 2015 article Cuenya and Ferreyra defined a class of functions in L-p-spaces, denoted by c(n)(p)(x). The class c(n)(p)(x) contains the class of L-p-differentiability functions, denoted by t(n)(p)(x), introduced in a 1961 article by Calderon-Zygmund. A more recent paper by Acinas, Favier and Zo introduced a new class of functions in Orlicz spaces L-Phi, called L-Phi-differentiable functions in the present article. The class of L-Phi-differentiable functions is closely related to the class t(n)(p)(x). In this work, we define a class of functions in L-Phi, denoted by c(n)(Phi)(x). The class c(n)(Phi)(x) is more general than the class of L-Phi-differentiable functions. We prove the existence of the best local F-approximation for functions in c(n)(Phi) (x) and study the convexity of the set of cluster points of the set of best Phi-approximations to a function on an interval when their measures tend to zero. 收起