A new kind of Durrmeyer-Stancu-type operators

Abstract The objective of this study is to examine a class of positive linear operators, defined in terms of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mi>b</m:mi> </m:mrow> <m:mrow> <m:mi>ψ</m:mi> <m:mo>,</m:mo> <m:mi>k</m:mi> </m:mrow> <m:mrow> <m:mi>λ</m:mi> <m:mo>,</m:mo> <m:mi>μ</m:mi> </m:mrow> </m:msubsup> </m:math> {b}_{\psi ,k}^{\lambda ,\mu } basis and to analyze their approximation properties. Direct estimates for the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>λ</m:mi> <m:mo>,</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(\lambda ,\mu ) -Durrmeyer-Stancu-type operators are obtained using the first modulus of continuity and in a certain Lipschitz-type space. Approximation properties of these operators in Lebesgue spaces are also given. Finally, illustrative graphics are provided to support the results and to compare the rate of convergence.