Topological Semivector Spaces Convexity And Fixed Point Theory
Topological Semivector Spaces Convexity And Fixed Point Theory
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Next, we illustrate how the spaces of concern arise naturally as certain hyperspaces of topological (semi-) vector spaces. Finally, we establish a number of fixed point and minmax theorems for topological semivector spaces with various local convexity properties. The fixed point results which we obtain here will be seen to generalize central fixed point theorems (for topological vector spaces) due to S. Kakutani [l94l], H. F. Bohnenblust & S. Karlin [l950] and K. Fan [l952j, which, in turn, are... generalizations of results due to L. E. J. Brouwer [l912], J. Schauder [l930] and A. Tychonoff [1935], respectively.
1. PRELIMINARIES Into this section we compress a quick review of some basic notions introduced and discussed in detail elsewhere [e. G. , see Prakash & Sertel, 1972].
In defining "semivector" spaces, the notion of a "left skew semlfield" serves as a catalyst. By a left skew semifield we mean a bimonoid in which is a group with zero distinct from its identity 1, is a comnutative semigroup with identity 0, and the (unitary) left action of
What to read after Topological Semivector Spaces Convexity And Fixed Point Theory?
You can find similar books in the "Read Also" column, or choose other free books by Prem Prakash to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Next, we illustrate how the spaces of concern arise naturally as certain hyperspaces of topological (semi-) vector spaces. Finally, we establish a number of fixed point and minmax theorems for topological semivector spaces with various local convexity properties. The fixed point results which we obtain here will be seen to generalize central fixed point theorems (for topological vector spaces) due to S. Kakutani [l94l], H. F. Bohnenblust & S. Karlin [l950] and K. Fan [l952j, which, in turn, are... generalizations of results due to L. E. J. Brouwer [l912], J. Schauder [l930] and A. Tychonoff [1935], respectively.
1. PRELIMINARIES Into this section we compress a quick review of some basic notions introduced and discussed in detail elsewhere [e. G. , see Prakash & Sertel, 1972].
In defining "semivector" spaces, the notion of a "left skew semlfield" serves as a catalyst. By a left skew semifield we mean a bimonoid in which is a group with zero distinct from its identity 1, is a comnutative semigroup with identity 0, and the (unitary) left action of
What to read after Topological Semivector Spaces Convexity And Fixed Point Theory?
You can find similar books in the "Read Also" column, or choose other free books by Prem Prakash to read onlineMoreLess
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