Cristina B. Corcino^1,2, Wilson D. Castañeda Jr.³, Roberto B. Corcino^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 133-151, 2022, DOI:10.32604/cmes.2022.019965

Abstract The tangent polynomials T_n (z) are generalization of tangent numbers or the Euler zigzag numbers T_n. In particular, T_n (0) = T_n. These polynomials are closely related to Bernoulli, Euler and Genocchi polynomials. One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostoltype polynomials. One of these Apostol-type polynomials is the Apostol-tangent polynomials T_n(z, λ). When λ = 1, T_n (z, 1) = T_n(z). The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and… More >

Mine Menekşe Yılmaz^*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 287-297, 2022, DOI:10.32604/cmes.2022.017385

Abstract The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of order α. Applying the Korovkin theorem, we arrive at the convergence of the operator with the aid of moments and central moments. We determine the rate of convergence of the operator using several tools such as -functional, modulus of continuity, second modulus of continuity. We also give a type of Voronovskaya theorem for estimating error. Moreover, we investigate some results about convergence properties of the operator in a weighted space. Finally, we give numerical examples to support our theorems… More >