Results 11 to 20 of about 1,829,120 (282)
A Note on the q-Derivative Operator [PDF]
Journal of Mathematical Analysis and Applications, 1993 We prove a formula for the nth power of the q-derivative operator at x=0 for every function whose nth derivative at x=0 exists. We give a proof in both the real variable and the complex variable case.
Koekoek, J., Koekoek, R.
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The q-derivative and applications to q-Szász Mirakyan operators
Calcolo, 2006 The article is devoted to investigation of so-called \(q\)-Szász Mirakyan operators introduced recently by one of the authors. These operators are defined in the following way. For \(f\in C\left[0,\infty\right)\), \(q\in\left(0,1\right)\) and each natural \(n\) \[ S_n^q\left(f;x\right)\equiv S_n^q\left(f\right)\left(x\right)= E_q\left(-\left[n\right]_q{
Aral, Ali, Gupta, Vijay
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Multivariable Tangent and Secant q-derivative Polynomials
, 2012 The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable $q$--environment. The $n$-th $q$-derivatives of the classical $q$-tangent and $q$-secant are each given two polynomial expressions.
Foata, Dominique, Han, Guo-Niu
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On Subclasses of Spiral-Like Functions Defined by the q-Derivative Operator
Journal of Function SpacesIn 1990, Ismail et al. introduced a generalized class of starlike functions using the q-derivative operator. Similarly, many authors have studied various subclasses of analytic functions involving the q-derivative operator from different perspectives ...
Fatma Z. El-Emam, Samar. M. Madian
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On q-Mocanu Type Functions Associated with q-Ruscheweyh Derivative Operator [PDF]
International Journal of Analysis and Applications, 2020 In this paper, we introduce certain subclasses of analytic functions defined by using the q-difference operator. Mainly we give several inclusion results for defined classes.
Khalida Inayat Noor, Shujaat Ali Shah
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Advances in Difference Equations, 2018 In this paper, we give the definitions of q,ω $q,\omega $-exponential function and q,ω $q,\omega $-gamma function. New concepts of fractional Hahn’s q,ω $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss
Yizhu Wang, Yiding Liu, Chengmin Hou
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Derivative observations in Gaussian Process models of dynamic systems [PDF]
, 2003 Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model.
Rasmussen, C.E. +4 more
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A new generalization of Mittag-Leffler function via q-calculus
Advances in Difference Equations, 2020 The present paper deals with a new different generalization of the Mittag-Leffler function through q-calculus. We then investigate its remarkable properties like convergence, recurrence relation, integral representation, q-derivative formula, q-Laplace ...
Raghib Nadeem +3 more
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On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems
Mathematics, 2020 A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every ...
Kin Keung Lai +2 more
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On $\Q$-Derived Polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2006 A -derived polynomial is a univariate polynomial, defined over the rationals, with the property that its zeros, and those of all its derivatives are rational numbers. There is a conjecture that says that -derived polynomials of degree 4 with distinct roots for themselves and all their derivatives do not exist.
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