Results 41 to 50 of about 117,000 (133)

Multiple Binomial‐Type Operators and Their Approximation Properties

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we introduce multiple binomial‐type operators (multiple Bernstein–Sheffer operators) and investigate their approximation properties. These properties are analyzed by means of a Korovkin‐type theorem. Furthermore, by using the first and second modulus of continuity together with Peetre’s κ‐functional, we establish the rate of convergence ...
Mehmet Ali Özarslan, Bayram Çekim, Sezin Çit, Smritijit Sen   +3 more
wiley   +1 more source

Error Estimation for Shifted q‐Szász–Kantorovich Operators and Their Numerical Properties

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper introduces a novel class of q‐Szász–Mirakjan–Kantorovich operators defined with shifted sequences. Utilizing the basic principles of q‐calculus, we design the King‐type fundamental construction of q‐Szász–Mirakjan–Kantorovich operators and derive their moments and central moments.
Md. Nasiruzzaman, Esmail Alshaban, Fahad Maqbul Alamrani, Adel Alatawi, M. Mursaleen, Smritijit Sen   +5 more
wiley   +1 more source

On the ψ− Sheffer F− Polynomials and Their Degenerate Matrices

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this study, we systematically construct a novel framework within umbral calculus by integrating the structures of generalized F‐calculus and degenerate sequences. Utilizing Roman’s foundational approach to umbral calculus, we first introduce a new family of ψ − F− linear functionals and their corresponding ψ − F− differential operators on the ...
Semra Kuş, Smritijit Sen
wiley   +1 more source

q-Difference equations for the 2-iterated q-Appell and mixed type q-Appell polynomials [PDF]

, 2018
In this article, the authors establish the recurrence relations and q-difference equations for the 2-iterated q-Appell polynomials. The recurrence relations and the q-difference equations for the 2-iterated q-Bernoulli polynomials, the q-Euler ...
H. M. Srivastava, Riyasat, Mumtaz, Khan, Subuhi, Subuhi Khan, Mumtaz Riyasat, Srivastava, H.M.   +5 more
core   +1 more source

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley   +1 more source

Appell and Sheffer sequences: on their characterizations through functionals and examples

Comptes Rendus. Mathématique, 2021
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the literature ...
Carrillo, Sergio A., Hurtado, Miguel
doaj   +1 more source

Two-Variable q-General-Appell Polynomials Within the Context of the Monomiality Principle

Mathematics
In this study, we consider the two-variable q-general polynomials and derive some properties. By using these polynomials, we introduce and study the theory of two-variable q-general Appell polynomials (2VqgAP) using q-operators.
Noor Alam, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo   +3 more
doaj   +1 more source

Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation

Studies in Applied Mathematics, Volume 154, Issue 3, March 2025.
ABSTRACT This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for general recurrence coefficients, as well as the stepline case, are provided for all these ...
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié‐Moreno, Manuel Mañas   +3 more
wiley   +1 more source

A unified matrix approach to the representation of Appell polynomials [PDF]

, 2014
In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix - a special matrix which has only the natural numbers as entries and is closely related to the ...
Tomaz, Graça, Malonek, Helmuth R., Aceto, L., Tomaz, G., Aceto, Lidia, Malonek, H. R.   +5 more
core   +1 more source

On the complex q-Appell polynomials [PDF]

, 2020
The purpose of this article is to generalize the ring of \(q\)-Appell polynomials to the complex case. The formulas for \(q\)-Appell polynomials thus appear again, with similar names, in a purely symmetric way.
Ernst, Thomas, Ernst, Thomas,, Thomas Ernst   +2 more
core   +2 more sources