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A new iteration method for the solution of third-order BVP via Green's function

Akgun Fatma Aydın, Rasulov Zaur

Demonstratio Mathematica

2021

Vol. 54, nr 1

425--435

In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.

Some properties of modified Szász-Mirakyan operators in polynomial spaces via the power summability method

Braha Naim L.

Journal of Applied Analysis

2020

Vol. 26, nr 1

79--90

In this paperwe will prove the Korovkin type theorem for modified Szász-Mirakyan operators via Astatistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem.

Direct and strong converse inequalities for approximation with Fejér means

Bustamante Jorge

Demonstratio Mathematica

2020

Vol. 53, nr 1

80--85

We present upper and lower estimates of the error of approximation of periodic functions by Fejér means in the Lebesgue spaces Lp2π. The estimates are given in terms of a K-functional for 1≤p≤∞ and in terms of the first modulus of continuity in the case 1

An investigation of the approximation of functions of two variables by the Poisson integral for Hermite expansions

Krech G.

Czasopismo Techniczne. Nauki Podstawowe

2014

R. 111, z. 3-NP

31--38

This paper presents a study of the approximation properties of the Poisson integral for Hermite expansions in the space Lp. The rate of convergence of functions of two variables by these integrals is established.

Artykuł poświęcony jest własnościom aproksymacyjnym całek Poissona związanych z wielomianami Hermite’a. Udowodniono twierdzenie o rzędzie zbieżności funkcji dwóch zmiennych w przestrzeni Lp tymi operatorami.