Add to ORKGThe topological complexity of sets of convex differentiable functions. Mohammed YAHDI Let C(x) be tSe set of alí convex arad continuous functions on a separable infinite dimensional Banach space X, equipped with tSe topolo~ ’ of uniform convengence on boranded subseta of>2. We show that tSe subset of alí convex Fréchet-diffenentiable franctions on 2<, and tSe subset of alt (not necessanily equivalent) FYéchet-differentiable norms on>2, reduce eveny coanalytic set, ira particular they are ¡mt Borel-sets.
AbstractUsing the extension of convex functions on a Banach space X to the bidual space X**, we intr...
Like differentiability, convexity is a natural and powerful property of functions that plays a signi...
summary:We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on $\Gamma$-...
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banac...
The main known results on differentiability of continuous convex operators ff from a Banach space XX...
AbstractLetN(X) be the set of all equivalent norms on a separable Banach spaceX, equipped with the t...
Abstract: Let X,Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed clos...
Let \(X\) be a Banach space. Let \(f(\cdot)\) be a real valued function defined on an open convex ...
One counterexample concerning the Fréchet differentiability of convex functions on closed set
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
Abstract. Modifying appropriately the method of a forgotten work [1], we show that if a continuous m...
We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex fu...
AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach spac...
The improved and expanded second edition contains expositions of some major results which have been ...
In this paper, we prove that if C⁎⁎ is a ε-separable bounded subset of X⁎⁎, then every convex functi...
AbstractUsing the extension of convex functions on a Banach space X to the bidual space X**, we intr...
Like differentiability, convexity is a natural and powerful property of functions that plays a signi...
summary:We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on $\Gamma$-...
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banac...
The main known results on differentiability of continuous convex operators ff from a Banach space XX...
AbstractLetN(X) be the set of all equivalent norms on a separable Banach spaceX, equipped with the t...
Abstract: Let X,Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed clos...
Let \(X\) be a Banach space. Let \(f(\cdot)\) be a real valued function defined on an open convex ...
One counterexample concerning the Fréchet differentiability of convex functions on closed set
Let X, Y be real Banach spaces. Let Z be a Banach space partially ordered by a pointed closed convex...
Abstract. Modifying appropriately the method of a forgotten work [1], we show that if a continuous m...
We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex fu...
AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach spac...
The improved and expanded second edition contains expositions of some major results which have been ...
In this paper, we prove that if C⁎⁎ is a ε-separable bounded subset of X⁎⁎, then every convex functi...
AbstractUsing the extension of convex functions on a Banach space X to the bidual space X**, we intr...
Like differentiability, convexity is a natural and powerful property of functions that plays a signi...
summary:We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on $\Gamma$-...