Approximation properties of Bezier-summation-integral type operators based on Polya–Bernstein functions

Voronovskaya‐type theorems for Urysohn type nonlinear Bernstein operators

“…For example, by considering discrete‐type probability distributions as a kernel functions of an approximation operators, such as Polya distribution, it is also possible to define Urysohn‐type linear or nonlinear forms of the summation‐type approximation operators . For further possibilities, please see Acu et al, Agrawal et al, and Deshwal et al…”

Approximation by Stancu-Durrmeyer type operators based on Pólya-Eggenberger distribution

“…introduced by Lupaş and Lupaş [15]. Concerning the operators (2) and 3, the reader is invited to see two recent papers [16], [17], where some results of the recalled operators are revised. Taking into account the period in which the Stancu operators (2) were introduced, we remark that there exists a huge interest to study them, respectively generalizations of them until nowadays.…”

“…Taking into account the period in which the Stancu operators (2) were introduced, we remark that there exists a huge interest to study them, respectively generalizations of them until nowadays. Some representative examples in this sense could be the papers of Razi [20], Finta [9], [10], Wang et al [22], Abel et al [1], Agrawal et al [2], [3], Gupta et al [13], [5], [14] and Deo et al [6]. Denote by L B [0, 1] the space of bounded Lebesgue integrable functions on [0, 1] and by Π n the space of polynomials of degree at most n ∈ N. In 2007, Pȃltȃnea [19] has introduced the following class of operators U n,ρ :…”

Blending type approximation by bézier-summation-integral type operators

“…Bézier-Bernstein type operators were established by many mathematicians. The pioneer works in this direction are due to [3,5,9,13,24,26,28,29,30]. In these works, the direct approximation results were obtained and the rate of convergence for functions of bounded variation were established.…”