Results 11 to 20 of about 8,549 (260)
Szász-Baskakov type operators based on q-integers [PDF]
Journal of Inequalities and Applications, 2014 Abstract In the present paper, we introduce the q-analog of the Stancu variant of Szász-Baskakov operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed.
Agrawal, Purshottam Narain +2 more
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On distribution of the number of semisimple rings of order at most x in an arithmetic progression [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let ℓ and q denote relatively prime positive integers. In this article, we derive the asymptotic formula for the summation Σ_{n≤x, n≡ℓ (mod q)} S(n), where S(n) denotes the number of non-isomorphic finite semisimple rings with n elements.
Thorranin Thansri +2 more
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Resonance between the Representation Function and Exponential Functions over Arithemetic Progression
Journal of Mathematics, 2021 Let rn denote the number of representations of a positive integer n as a sum of two squares, i.e., n=x12+x22, where x1 and x2 are integers. We study the behavior of the exponential sum twisted by rn over the arithmetic progressions ∑n∼Xn≡lmodqrneαnβ ...
Li Ma, Xiaofei Yan
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Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 This work is a first step towards a theory of "$q$-deformed complex numbers". Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible with
Valentin Ovsienko
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A note on type 2 q-Bernoulli and type 2 q-Euler polynomials
Journal of Inequalities and Applications, 2019 As is well known, power sums of consecutive nonnegative integers can be expressed in terms of Bernoulli polynomials. Also, it is well known that alternating power sums of consecutive nonnegative integers can be represented by Euler polynomials.
Dae San Kim +3 more
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The q-Integers and the Mersenne Numbers [PDF]
SSRN Electronic Journal, 2018 Here we will show that the q-integers, the q-analogue of the integers that we can find in the q-calculus, are forming an additive group having a generalized sum similar to the sum of the Tsallis q-entropies of independent systems. The symmetric form of q-integers will be studied too.
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Rational Operators Based on q-Integers
Results in Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amato Umberto, Della Vecchia Biancamaria
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A new type of Szász–Mirakjan operators based on q-integers
Journal of Inequalities and Applications, 2023 AbstractIn this article, by using the notion of quantum calculus, we define a new type Szász–Mirakjan operators based on the q-integers. We derive a recurrence formula and calculate the moments $\Phi _{n,q}(t^{m};x)$ Φ n , q
Sabancigil, Pembe +2 more
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The Numerical Evaluation Methods for Beta Function
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2022 In this study, the beta function that is encountered in computational mathematics and physics is analyzed. The correct evaluation of this function also affects the accuracy of other mathematical functions in quantum mechanical calculations. Especially in
Sılay Aytaç Yükçü
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Some bivariate Durrmeyer operators based on q-integers [PDF]
Journal of Mathematical Inequalities, 2017 Summary: In the present paper we introduce a \(q\)-analogue of the bivariate Durrmeyer operators. A convergence theorem for these operators is established and the rate of convergence in terms of modulus of continuity is determined. Also, a Voronovskaja type theorem has been investigated for these operators.
Bărbosu, Dan +2 more
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