On the Approximation Properties of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
                     <mi>q</mi>
                     <mo>−</mo>
                  </math>Analogue Bivariate <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2">
                     <mi>λ</mi>
                  </math>-Bernstein Type Operators

AbstractAlthough private or community initiatives for biodiversity conservation (such as land trusts) have a strong tradition in many countries, rigorous evidence of recently evolved movements in post-socialist countries is missing. This study describes the evolution of Czech land trust movement and analyses their representatives’ motivation for engagement in biodiversity conservation. It also investigates the intensity of interaction among public and land trust conservation efforts. For this purpose, we identified localities in which the territory managed by Czech land trusts overlaps with small-scale public nature reserves managed by regional governments. We conducted semi-structured face-to-face interviews with representatives of all NGOs and regional officials in-charge. Our qualitative analysis revealed that some regional biodiversity conservation officials see land trusts as partners, but others are rather indifferent to, or uninformed about, their activities. Additionally, land trust representatives see themselves as complementing the public effort: their main motivation for engagement is to facilitate biodiversity conservation in addition to the public provision.

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On the rate of convergence of modified $\alpha$-Bernstein operators based on q-integers

Agrawal

Kumar

Baxhaku³

2022

J. Numer. Anal. Approx. Theory

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In the present paper we define a q-analogue of the modified a-Bernstein operators introduced by Kajla and Acar (Ann. Funct. Anal. 10 (4) 2019, 570-582). We study uniform convergence theorem and the Voronovskaja type asymptotic theorem. We determine the estimate of error in the approximation by these operators by virtue of second order modulus of continuity via the approach of Steklov means and the technique of Peetre's $K$-functional. Next, we investigate the Gruss- Voronovskaya type theorem. Further, we define a bivariate tensor product of these operatos and derive the convergence estimates by utilizing the partial and total moduli of continuity. The approximation degree by means of Peetre's K- functional , the Voronovskaja and Gruss Voronovskaja type theorems are also investigated. Lastly, we construct the associated GBS (Generalized Boolean Sum) operator and examine its convergence behavior by virtue of the mixed modulus of smoothness.

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On the Approximation Properties of $q -$ Analogue Bivariate $λ$ -Bernstein Type Operators

Abstract: In this article, we establish an extension of the bivariate generalization of the q -Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q -Bernstein type. For the first operators, we stat… Show more

Cited by 3 publications

References 20 publications

Batch-sequential design and heteroskedastic surrogate modeling for delta smelt conservation

Batch-sequential design and heteroskedastic surrogate modeling for delta smelt conservation

Public and community conservation of biodiversity—rivalry or cooperation?

On the rate of convergence of modified \(\alpha\)-Bernstein operators based on q-integers

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On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

Abstract: In this article, we establish an extension of the bivariate generalization of the q -Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q -Bernstein type. For the first operators, we stat… Show more

Cited by 3 publications

References 20 publications

Batch-sequential design and heteroskedastic surrogate modeling for delta smelt conservation

Batch-sequential design and heteroskedastic surrogate modeling for delta smelt conservation

Public and community conservation of biodiversity—rivalry or cooperation?

On the rate of convergence of modified \(\alpha\)-Bernstein operators based on q-integers

Contact Info

Product

Resources

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On the Approximation Properties of $q -$ Analogue Bivariate $λ$ -Bernstein Type Operators