Bézier-Summation-Integral-Type Operators That Include Pólya–Eggenberger Distribution

Abstract

We define the summation-integral-type operators involving the ideas of Pólya–Eggenberger distribution and Bézier basis functions, and study some of their basic approximation properties. In addition, by means of the Ditzian–Totik modulus of smoothness, we study a direct theorem as well as a quantitative Voronovskaja-type theorem for our newly constructed operators. Moreover, we investigate the approximation of functions with derivatives of bounded variation (DBV) of the aforesaid operators.

Higher Transcendental Functions and Their Multi-Disciplinary Applications

“…The geographical distribution of the contributors to this Special Issue is remarkably widely-scattered. Their contributions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]) originated in many different countries on every continent of the world.…”

“…The subject matter of the first 16 publications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]) dealt extensively with analytic, univalent, multivalent, and harmonic functions of complex analysis and their quantum or basic (or q-) extensions, the Euler-Poisson-Darboux partial differential equation, approximation theory and associated summability methods, variational inequalities, linear and nonlinear integro-differential equations, growth results involving Dirichlet series, theory and applications of wavelet transforms, analysis of ordinary and partial differentialdifference equations, and several other topics listed in the preceding section.…”

On the Approximation by Bivariate Szász–Jakimovski–Leviatan-Type Operators of Unbounded Sequences of Positive Numbers

“…There are many published articles related to these works, for example, those by Kajla et al [7], Mursaleen et al [8][9][10][11], Mohiuddine et al [12][13][14][15][16], Nasiruzzaman et al [6,[17][18][19][20][21][22], Özger et al [23]. For studies on Bernstein and Szász types operators involving the idea of Chlodowsky and Charlier polynomials, we refer to [24][25][26][27][28].…”