Weighted convolutions associated with probability functions and Bernstein polynomials

Abstract

The weighted convolution inequalities for power series and their consequences are presented in terms of various probability functions. The complete description of the related extreme cases is given. It culminates with a limit binomial theorem involving Bernstein's polynomial sequences. Some probabilistic interpretation and examples are discussed.

Keywords:

• convolutions
• inequalities for sums, series and integrals
• negative binomial coefficients
• Bernstein polynomials
• probability functions
• expectations

2000 Mathematics Subject Classification:

• 26D15
• 33B15
• 11B65
• 60E05
• 41A10

Acknowledgements

This research was conducted at the University of South Florida.

Disclosure statement

No potential conflict of interest was reported by the author.