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New inequalities of CBS-type for power series of complex numbers

100%

Dragomir S. S.

tom Nr 57

37--51

Let [formula] be a function defned by power series with complex coefficients and convergent on the open disk D (0, R) C, R > 0. In this paper we show amongst other that, if α, z C are such that |α|, |α||z| < R, then [formula] where [formula]. Aplications for some fundamental functions defined by power series are also provided. be a function defned by power series with complex coefficients and convergent on the open disk D(0, R) C, R > 0. In this paper we show amongst other that, if α, z C are such that |α|, |α||z| < R, then [formula] where Applications for some fundamental functions defined by power series are also provided.

Power series solution of first order matrix differential equations

100%

Kukla S. , Zamorska I.

tom Vol. 13, nr 3

123--128

In the paper, the solution of second order differential equations with various coefficients is presented. The concerning equations are written as first order matrix differential equations and solved with the use of the power series method. Examples of application of the proposed method to the equations occurring in the technical problems are presented.

Some gap power series in multidimensional setting

70%

Siciak J.

nr 2

We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.

On the Behavior of Power Series with Completely Additive Coefficients

60%

Petrushov O.

2015

tom Vol. 63, no. 3

217--225

Consider the power series A(z)=∑∞n=1 α (n) zn, where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity e2πil/q. We give effective omega-estimates for A(e(l/pk)r) when r→1−. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.

Korovkin-type approximation by operators in Riesz spaces via power series method

51%

Chil E. , Assili M.

2019

tom Vol. 52, nr 1

490--495

In this paper we prove an Ozguç, Yurdakadim and Taş version of the Korovkin-type approximation by operators in the sense of the power series method. That is, we try to extend the Korovkin approximation theorems, obtained by Ozguç and Taş in 2016, and Taş and Yurdakadim in 2017, for concrete classes of Banach spaces to the class of Riesz spaces. Some applications are presented.