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...

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive Voronovskaya-type asymptotic theorem for this type of operator. Then, local global theorems are obtained by using classical modulus continuity K-functional. Finally, rate convergence functions with a derivative bounded variation. The results show that new have g...

The present paper deals with the approximation properties for exponential functions of general Durrmeyer type operators having weights Sz?sz basis functions. Here we give explicit expressions moments by means which establish, derivatives operators, Voronovskaja formulas growth and corresponding weighted quantitative estimates remainder in simultaneous approximation.

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...