On Generalization of Beta Operators | ||
| basrah journal of science | ||
| Article 4, Volume 34, Issue 3, December 2016, Pages 33-44 PDF (0 K) | ||
| Authors | ||
| Rihab R. Abdul-Rezaq; Ali J. Mohammad; | ||
| Abstract | ||
| In this present paper, we introduce a generalization definition to Beta weight functions depend on a non-negative integer r called r-Beta. This definition restricts to the classical Lupas and to the classical Beta weight functions whenever r=0,1 respectively. In addition, we used these weight functions to define two operators of summation and of summation-integral types. Surly, these operators restrict to the classical Lupas operators and to the classical Beta operators of both summation and summation-integral types whenever r=0,1 respectively. In addition, we can get the mixed operators of Lupas-Beta and Beta-Lupas for a suitable chose of integer values. Furthermore, we derive a Voronovaskaja-type asymptotic formula for the new operators from which we can get the similar formulas for many operators of summation and summation-integral types of mixed Lupas-Beta (or Beta-Lupas) weight functions and more. | ||
| Keywords | ||
| Linear positive operators; Beta operators; Lupas operators; Voronovaskaja; type asymptotic formula | ||
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