Abstract Employing some properties of multivariate Baskakov–Durrmeyer operators and utilizing modified K -functional a decomposition technique, the authors obtain direct theorem weak type inverse in Orlicz spaces.

We constructed a summation–integral type operator based on the latest research in linear positive operators area. establish some approximation properties for this new operator. highlight qualitative part of presented operator; we studied uniform convergence, Voronovskaja-type theorem, and Grüss–Voronovskaja result. Our subsequent study focuses direct theorem using Ditzian–Totik modulus smoothne...

In the present paper we introduce the GBS (Generalized Boolean Sum) operators of Durrmeyer type based on q -integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical c...

In the present paper, we introduce a new type of Bernstein-Durrmeyer operators preserving linear functions in movable interval. The approximation rate for continuous and Voronovskaja?s asymptotic estimate are obtained.

In the present paper, we introduce genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. also second order central moment Znq,α((t−x)2;x). give Korovkin-type theorem; estimate rate convergence continuous functions. Furthermore, prove local approximation theorem in terms modulus continuity; ...

<p style='text-indent:20px;'>In the present paper, we introduce a new type of Bernstein-Durrmeyer operators preserving linear functions in movable interval. The approximation rate for continuous and Voronovskaja's asymptotic estimate are obtained.</p>