Abstract: Let X,Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex cone K. Let f(·) be a locally uniformly approximate convex function mapping an open subset ΩY ⊂ Y into Z. Let ΩX ⊂ X be an open subset. Let σ(·) be a differentiable mapping of ΩX into ΩY such that the differentials of σ x are locally uniformly continuous function of x. Then f(σ(·)) mapping X into Z is also a locally uniformly approximate convex function. Therefore, in the case of Z = Rn the composed function f(σ(·)) is Fréchet differentiable on a dense Gδ-set, provided X is an Asplund space, and Gateaux differentiable on a dense Gδ-set, provided X is separable. As a consequence, we obtain that in the case of Z = Rn a locally uniform...
The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Ban...
1. Let X, Y be real normed vector spaces. A function/from a subset of X into 7 is said to be (Fre*ch...
AbstractLet Π be a collection of subsets of a compact set S in a normed linear space and K be all co...
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
We show that if X is a Banach space whose dual X* has an equivalent locally uniformly rotund (LUR) n...
AbstractThis paper shows that every w*-lower semicontinuous Lipschitzian convex function on the dual...
AbstractThis paper shows that every extended-real-valued lower semi-continuous proper (respectively ...
Let \(X\) be a Banach space. Let \(f(\cdot)\) be a real valued function defined on an open convex ...
AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach spac...
In the paper the equivalence of the notions of uniformly approximate convex functions and strongly a...
This book presents the evolution of uniform approximations of continuous functions. Starting from th...
AbstractIn this paper, which is a continuation of Timofte (J. Approx. Theory 119 (2002) 291–299, we ...
AbstractIn this paper, we give special uniform approximations of functions u from the spaces CX(T) a...
The present paper is concerned with some properties of functions with values in locally convex vecto...
AbstractThis paper considers Fréchet differentiability almost everywhere in the sense of category of...
The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Ban...
1. Let X, Y be real normed vector spaces. A function/from a subset of X into 7 is said to be (Fre*ch...
AbstractLet Π be a collection of subsets of a compact set S in a normed linear space and K be all co...
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
We show that if X is a Banach space whose dual X* has an equivalent locally uniformly rotund (LUR) n...
AbstractThis paper shows that every w*-lower semicontinuous Lipschitzian convex function on the dual...
AbstractThis paper shows that every extended-real-valued lower semi-continuous proper (respectively ...
Let \(X\) be a Banach space. Let \(f(\cdot)\) be a real valued function defined on an open convex ...
AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach spac...
In the paper the equivalence of the notions of uniformly approximate convex functions and strongly a...
This book presents the evolution of uniform approximations of continuous functions. Starting from th...
AbstractIn this paper, which is a continuation of Timofte (J. Approx. Theory 119 (2002) 291–299, we ...
AbstractIn this paper, we give special uniform approximations of functions u from the spaces CX(T) a...
The present paper is concerned with some properties of functions with values in locally convex vecto...
AbstractThis paper considers Fréchet differentiability almost everywhere in the sense of category of...
The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Ban...
1. Let X, Y be real normed vector spaces. A function/from a subset of X into 7 is said to be (Fre*ch...
AbstractLet Π be a collection of subsets of a compact set S in a normed linear space and K be all co...