Gene

Ecology

Bernstein polynomial

Pure mathematics

Biology

Applied mathematics

Biochemistry

Computer science

Lipschitz continuity

Computer network

Type (biology)

Modulus of continuity

Mathematics

Smoothness

Rate of convergence

Transcription factor

Mathematical analysis

Repressor

Chemistry

Channel (broadcasting)

Operator (biology)

Operator theory

Generalization

An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of Bernstein–Kantorovich operators involving shape parameters λ, α and a positive integer as an original extension of Bernstein–Kantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.

Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators