Inequalities based on a generalization of concavity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Inequalities based on a generalization of concavity

Authors:	Paul W. Eloe Johnny Henderson

Affiliation:	Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316 ; Department of Mathematics, 218 Parker Hall, Auburn University, Alabama 36849-5310

Abstract:	The concept of concavity is generalized to functions, , satisfying order differential inequalities, $(-1)^{n-k}y^{(n)}(t)ge 0, 0le tle 1$ , and homogeneous two-point boundary conditions, $y(0)=ldots =y^{(k-1)}(0)=0, y(1)=ldots =y^{(n-k-1)}(1)=0$ , for some . A piecewise polynomial, which bounds the function, , below, is constructed, and then is employed to obtain that $y(t)ge \|\|y\|\|/4^{m}, 1/4le tle 3/4$ , where max and denotes the supremum norm. An analogous inequality for a related Green's function is also obtained. These inequalities are useful in applications of certain cone theoretic fixed point theorems.

Keywords:	Differential inequalities

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