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On zeros and fixed points of multifunctions with non-compact convex domains

Sehie Park, Jong Sook Bae (1993)

Commentationes Mathematicae Universitatis Carolinae

Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave functions on convex spaces, we obtain extended versions of the existence theorem of H. Ben-El-Mechaiekh [2] on zeros for multifunctions with non-compact domains, the coincidence theorem of S.H. Kum [5] for upper hemicontinuous multifunctions, and the Ky Fan type fixed point theorems due to E. Tarafdar [13].

On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions

S. Rolewicz (1999)

Studia Mathematica

Let (X,d) be a metric space. Let Φ be a family of real-valued functions defined on X. Sufficient conditions are given for an α(·)-monotone multifunction $Γ : X \to 2^{Φ}$ to be single-valued and continuous on a weakly angle-small set. As an application it is shown that a γ-paraconvex function defined on an open convex subset of a Banach space having separable dual is Fréchet differentiable on a residual set.

One counterexample concerning the Fréchet differentiability of convex functions on closed sets

Eva Matoušková (1993)

Acta Universitatis Carolinae. Mathematica et Physica

Displaying 21 – 23 of 23

On zeros and fixed points of multifunctions with non-compact convex domains

On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions

One counterexample concerning the Fréchet differentiability of convex functions on closed sets

Currently displaying 21 – 23 of 23