the aim of this paper is to study the behaviour of certain sequence of nonlinear durrmeyer operators $nd_{n}f$ of the form $$(nd_{n}f)(x)=intlimits_{0}^{1}k_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{n}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% k_{n}left( x,t,uright) $ satisfies some suitable assumptions. here we estimate the rate...

In the present paper we give the rate of convergence for the linear combinations of the generalized Durrmeyer type operators which includes the well known Szasz-Durrmeyer operators and Baskakov-Durrmeyer operators as special cases.

In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...

In the present note, we introduce a Bezier variant of a new type of Bernstein Durrmeyer operator, which was introduced by Gupta [3]. We estimate the rate of convergence by using the decomposition technique of functions of bounded variation and applying the optimum bound. It is observed that the analysis for our Bezier variant of new Bernstein Durrmeyer operators is different from the usual Bern...

This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators $(NBD_{n})$ the form \[ (NBD_{n})(f;x) =\int_{0}^\infty K_{n}(x,t,f(t))\,dt \] with $x\in [0,\infty)$ and $n\in\mathbb{N}$. While $K_{n}(x,t,u)$ provide convenient assumptions, these work on bounded functions, which are defined all finite subintervals $[0,\infty)$. comprise some pointwise convergence results f...

In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absol...

Keywords: Baskakov–Durrmeyer operator Pointwise convergence Asymptotic formula q-Analogue a b s t r a c t In this paper, we are dealing with a new type of Baskakov–Durrmeyer–Stancu (BDS) operators D ða;bÞ n ðf ; xÞ defined by (1.4). First we estimate moments of these operators and also obtain the recurrence relations for the moments. We estimate some approximation properties and asymptotic form...

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate...