A LOWER BOUND FOR THE DELTA-NIELSEN NUMBER

A LOWER BOUND FOR THE DELTA-NIELSEN NUMBER

This paper is concerned with the number of solutions of three kinds of equations. Let f,g : X approaches Y and h : X approaches X be maps, and let y sub 0 be a member of Y. The equations we will study are (1) f(x) = g(x), (2) f(x) = y sub 0, and (3) h(x) = x. In a previous paper, the first author de...

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Hauptverfasser: Brooks,Robin B. S, Brown,Robert F
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EQUATIONS
HAUSDORFF SPACE
MAPPING(TRANSFORMATIONS)
MATHEMATICS
Numerical Mathematics
THEOREMS
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description This paper is concerned with the number of solutions of three kinds of equations. Let f,g : X approaches Y and h : X approaches X be maps, and let y sub 0 be a member of Y. The equations we will study are (1) f(x) = g(x), (2) f(x) = y sub 0, and (3) h(x) = x. In a previous paper, the first author defined a lower bound N for the number of solutions of these equations which remains such a lower bound when f,g, and h are moved through homotopies. The number N is called the Delta-Nielsen number of the equation. Prepared in cooperation with California Univ., Los Angeles, under Grant NSF-GP-4018.
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Let f,g : X approaches Y and h : X approaches X be maps, and let y sub 0 be a member of Y. The equations we will study are (1) f(x) = g(x), (2) f(x) = y sub 0, and (3) h(x) = x. In a previous paper, the first author defined a lower bound N for the number of solutions of these equations which remains such a lower bound when f,g, and h are moved through homotopies. The number N is called the Delta-Nielsen number of the equation. 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S ; Brown,Robert F</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-dtic_stinet_AD06563063</frbrgroupid><rsrctype>reports</rsrctype><prefilter>reports</prefilter><language>eng</language><creationdate>1967</creationdate><topic>EQUATIONS</topic><topic>HAUSDORFF SPACE</topic><topic>MAPPING(TRANSFORMATIONS)</topic><topic>MATHEMATICS</topic><topic>Numerical Mathematics</topic><topic>THEOREMS</topic><toplevel>online_resources</toplevel><creatorcontrib>Brooks,Robin B. S</creatorcontrib><creatorcontrib>Brown,Robert F</creatorcontrib><creatorcontrib>RAND CORP SANTA MONICA CALIF</creatorcontrib><collection>DTIC Technical Reports</collection><collection>DTIC STINET</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Brooks,Robin B. 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subjects EQUATIONS
HAUSDORFF SPACE
MAPPING(TRANSFORMATIONS)
MATHEMATICS
Numerical Mathematics
THEOREMS
title A LOWER BOUND FOR THE DELTA-NIELSEN NUMBER
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