منابع مشابه
Stability of generalized QCA-functional equation in P-Banach spaces
In this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.
متن کاملOn P- and p-Convexity of Banach Spaces
and Applied Analysis 3 Lemma 2.7 Goebel-Kirk . Let X be a Banach space. For each ε ∈ ε0 X , 2 , one has the equality δX 2 − 2δX ε 1 − ε/2. Lemma 2.8 Ullán . Let X be a Banach space. For each 0 ≤ ε2 ≤ ε1 < 2 the following inequality holds: δX ε1 − δX ε2 ≤ ε1 − ε2 / 2 − ε1 . Using these lemmas we obtain: Theorem 2.9. Let X be a Banach space which satisfies δX 1 > 0, that is, ε0 X < 1. Then X is P...
متن کاملRolle’s Theorem Is Either False or Trivial in Infinite-dimensional Banach Spaces
We prove the following new characterization of C (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a C smooth (Lipschitz) bump function if and only if it has another C smooth (Lipschitz) bump function f such that f ′(x) 6= 0 for every point x in the interior of the support of f (that is, f does not satisfy Rolle’s theorem). Moreover, the support of this bump ca...
متن کاملBanach Spaces
(A revised and expanded version of these notes are now published by Springer.) 1 Banach Spaces Definition A normed vector space X is a vector space over R or C with a function called the norm. 1. The set of real numbers with the norm taken to be the absolute value.
متن کاملBanach Spaces
Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/notes 2012-13/05 banach.pdf] 1. Basic definitions 2. Riesz’ Lemma 3. Counter-example: non-existence of norm-minimizing element 4. Normed spaces of continuous linear maps 5. Dual spaces of normed spaces 6. Banach-Steinhaus/uniform-boundedness theorem 7. Open mapping theore...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1972
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-43-1-1-25