Explicit and Implicit Complementarity Problems in a Hilbert Space

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K-metric and K-normed linear spaces: survey

We give a short survey on some fixed point theorems which are generalizations of the classical Banach-Caccioppoli principle of contractive mappings. All these results are gathered in three theorems about existence and uniqueness of fixed points for operators which act in K-metric or K-normed linear spaces and, in particular, in local convex spaces and scales of Banach spaces. Three fixed point theorems presented in this article cover numerous applications in numerical methods, theory of integral equations, some results on iterative methods for construction of periodic solution to ordinary differential equations, existence and uniqueness results on solvability for Cauchy and Goursat problems of Ovsjannikov-Treves-Nirenberg type and so on

On the \Cal L-characteristic of fractional powers of linear operators

summary:We describe the geometric structure of the {\Cal L}-characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss-\linebreak Ovchinnikov interpolation theorems, as well as on the Krasnosel'skij-Krejn factorization theorem