Iterative solution of nonlinear equations of the pseudo-monotone type in Banach spaces

A. M. Saddeek; Sayed A. Ahmed

Non-compact perturbations of $m$ -accretive operators in general Banach spaces

Mieczysław Cichoń (1992)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we deal with the Cauchy problem for differential inclusions governed by $m$ -accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x^{'} (t) \in - A x (t) + f (t, x (t))$ , $x (0) = x_{0}$ , where $A$ is an $m$ -accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let $D$ be a nonempty compact subset of a Banach space $X$ and denote by $S (X)$ the family of all nonempty bounded closed convex subsets of $X$ . We endow $S (X)$ with the Hausdorff metric and show that there exists a set $ℱ \subset S (X)$ such that its complement $S (X) ∖ ℱ$ is $σ$ -porous and such that for each $A \in ℱ$ and each $\tilde{x} \in D$ , the set of solutions of the best approximation problem $∥ \tilde{x} - z ∥ \to min$ , $z \in A$ , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

Displaying similar documents to “Iterative solution of nonlinear equations of the pseudo-monotone type in Banach spaces”

Non-compact perturbations of m -accretive operators in general Banach spaces

Best approximations and porous sets

Non-compact perturbations of $m$ -accretive operators in general Banach spaces