Entropies and Heun functions associated with positive linear operators

Raşa, Ioan

doi:10.1016/j.amc.2015.06.085

Cited by 20 publications

(41 citation statements)

References 18 publications

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“…1 in [7]) we immediately obtain the following corollary. This was conjectured recently (but not necessarily only for c > 0) by I. Raşa in Conjecture 7.1 in [14].…”

Section: Sums Of Squared Baskakov Functionsmentioning

confidence: 63%

“…Recently, there has been an increasing interest in monotonicity and convexity properties of sums of squared basis functions arising in approximation theory (see, e.g., [10], [12], [8], [14]). Among the classical approximation operators usually studied in this context we find operators constructed using the basis of Bernstein polynomials, the Mirakjan-Favard-Szász basis, the Meyer-König and Zeller basis, the Lagrange basis, the Bleimann-Butzer-Hahn basis and the Baskakov basis.…”

Section: Introductionmentioning

confidence: 99%

“…The first one gives a monotonicity result on the complete elliptic integral of the first kind. Next, we deal with the a recent conjecture of I. Raşa stating the following (see Conjecture 7.1 in [14]):…”

Section: Introductionmentioning

confidence: 99%

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Complete monotonicity and zeros of sums of squared Baskakov functions

Abel

Gawronski

Neuschel

2015

Applied Mathematics and Computation

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Keywords:Baskakov operator Complete monotonicity Convexity Chebyshev-Grüss-type inequality Distribution of zeros Complete elliptic integral of the first kind a b s t r a c tWe prove complete monotonicity of sums of squares of generalized Baskakov basis functions by deriving the corresponding results for hypergeometric functions. Moreover, in the central Baskakov case we study the distribution of the complex zeros for large values of a parameter. We finally discuss the extension of some results for sums of higher powers.

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“…1 in [7]) we immediately obtain the following corollary. This was conjectured recently (but not necessarily only for c > 0) by I. Raşa in Conjecture 7.1 in [14].…”

Section: Sums Of Squared Baskakov Functionsmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

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Complete monotonicity and zeros of sums of squared Baskakov functions

Abel

Gawronski

Neuschel

2015

Applied Mathematics and Computation

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“…For c < 0, S n,c is convex on 0, − 1 c . A stronger conjecture was formulated in [14] and [17]: It was validated for c ≥ 0 by U. Abel, W. Gawronski and Th. Neuschel [1], who proved a stronger result:…”

Section: Rényi Entropy and Tsallis Entropymentioning

confidence: 96%

Complete monotonicity of some entropies

Raşa

2016

Period Math Hung

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“…Let us mention that the "degree of nonmultiplicativity" of the operator L can be estimated in terms of the information potential S(x): see [17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Inequalities for Information Potentials and Entropies

et al. 2020

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We consider a probability distribution p0(x),p1(x),… depending on a real parameter x. The associated information potential is S(x):=∑kpk2(x). The Rényi entropy and the Tsallis entropy of order 2 can be expressed as R(x)=−logS(x) and T(x)=1−S(x). We establish recurrence relations, inequalities and bounds for S(x), which lead immediately to similar relations, inequalities and bounds for the two entropies. We show that some sequences Rn(x)n≥0 and Tn(x)n≥0, associated with sequences of classical positive linear operators, are concave and increasing. Two conjectures are formulated involving the information potentials associated with the Durrmeyer density of probability, respectively the Bleimann–Butzer–Hahn probability distribution.

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Entropies and Heun functions associated with positive linear operators

Cited by 20 publications

References 18 publications

Complete monotonicity and zeros of sums of squared Baskakov functions

Complete monotonicity and zeros of sums of squared Baskakov functions

Complete monotonicity of some entropies

Inequalities for Information Potentials and Entropies

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