Rate of convergence of exponential type operators related to $$p\left( x\right) =2x^{3/2}$$ for functions of bounded variation

Abstract

The present article deals with the approximation of certain exponential type operators defined by Ismail and May. We estimate the rate of convergence of these operators for functions of bounded variation.

Some inequalities and numerical results estimating error of approximation for tensor product kind bivariate quantum beta-type operators and pertaining to GBS variant

“…Lastly, this study can be extended to the following future problems. By considering the reference [15], A-statistical convergence of the bivariate beta-type operators can be investigated; by using the definition of post-quantum beta function and post-quantum gamma function in [16], a post-quantum analogue of the bivariate quantum beta-type operators can be defined and its approximation properties can be investigated; and by considering the reference [17], a bivariate exponential beta-type operator can be defined and its approximation properties can be investigated.…”

Convergence of Special Sequences of Semi-Exponential Operators

“…(B) The exponential operators are constructed using a differential equation. Modifying this equation, the so-called semi-exponential operators are introduced (see [8,[16][17][18]20]).…”

The convergence of exponential operators connected with x^3 on functions of bounded variation

“…The convergence rate on functions of bounded variation is also an important area of research in the recent past decades, we mention here some of the work done earlier on different operators viz. Bézier variant of the Baskakov-Kantorovich operators [1], exponential operators connected with p(x) = 2x 3/2 [2], MKZ operators [3], Baskakov-Durrmeyer type operators [4], Baskakov Bézier operators [5], nonlinear integral operators [12], Bézier variant of the Bleimann-Butzer-Hahn operators [14], Kantorovich variant of the Bleimann, Butzer and Hahn operators [18], Szász-Bézier integral operators [17], general family of operators of Durrmeyer type [15] etc. Also some better bounds to have different basis were established in [19].…”