Some new generalized G-KKM and generalized S-KKM theorems are proved under the noncompact setting of generalized convex spaces. As applications, some new minimax inequalities, saddle point theorems, a coincidence theorem, and a fixed point theorem are given in generalized convex spaces. These theore
Generalized approximation spaces and applications
β Scribed by Jose Maria Almira; Uwe Luther
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 427 KB
- Volume
- 263-264
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
In the paper we generalize the theory of classical approximation spaces to a much wider class of spaces which are defined with the help of best approximation errors. We also give some applications. For example, we show that generalized approximation spaces can be used to find natural (in some sense) domains of definition of unbounded operators. (Β© 2004 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
π SIMILAR VOLUMES
We develop a simple geometry free context where one can formulate and prove general forms of Gehring's Lemma. We show how our result follows from a general inverse type reiteration theorem for approximation spaces.
In this paper some parametric types of KKM theorems are established in generalized interval spaces. As applications, we utilize these results to obtain some new minimax theorems, section theorems, and existence theorems of solutions for variational inequalities. The results presented in this paper n