An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions

S. Rolewicz. "An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions." Studia Mathematica 172.3 (2006): 243-248. <http://eudml.org/doc/285160>.

@article{S2006,
abstract = {Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that $f(tx + (1-t)y) ≤ tf(x) + (1-t)f(y) + min[t,(1-t)]α(||x-y||)$. Then there is a dense $G_\{δ\}$-set $A_\{G\} ⊂ Ω$ such that f is Gateaux differentiable at every point of $A_\{G\}$.},
author = {S. Rolewicz},
journal = {Studia Mathematica},
keywords = {Gâteaux differentiability; strongly -paraconvex functions},
language = {eng},
number = {3},
pages = {243-248},
title = {An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions},
url = {http://eudml.org/doc/285160},
volume = {172},
year = {2006},
}

TY - JOUR
AU - S. Rolewicz
TI - An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions
JO - Studia Mathematica
PY - 2006
VL - 172
IS - 3
SP - 243
EP - 248
AB - Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that $f(tx + (1-t)y) ≤ tf(x) + (1-t)f(y) + min[t,(1-t)]α(||x-y||)$. Then there is a dense $G_{δ}$-set $A_{G} ⊂ Ω$ such that f is Gateaux differentiable at every point of $A_{G}$.
LA - eng
KW - Gâteaux differentiability; strongly -paraconvex functions
UR - http://eudml.org/doc/285160
ER -