SOME MEAN SQUARE INTEGRAL INEQUALITES INVOLVING THE BETA FUNCTION AND GENERALIZED CONVEX STOCHATIC PROCESSES

SOME MEAN SQUARE INTEGRAL INEQUALITES INVOLVING THE BETA FUNCTION AND GENERALIZED CONVEX STOCHATIC PROCESSES

J. E. H. Hernandez, J. F. Gomez

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Abstract

In the present work some integral inequalities which involve the Beta function for stochastic processes whose absolute values posses the property of convexity, or P????convexity or s????convexity in the second sense are established. In the same way some others integral inequalities for stochastic processes whose k????th powers of its absolute values posses these kind of generalized convexity are established making use of the Holder's inequality and power mean inequality.

Keywords

Mean square integral inequalities, convex stochastic processes, beta function.