We construct Kantorovich variant of generalized Sz?sz-Mirakjan operators whose construction depends on a continuously differentiable, increasing and unbounded function ?. For these new we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

we will apply the successive approximation method forproving the hyers--ulam stability of a linear integral equation ofthe second kind.

The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012). We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with...

This research paper is an introduction to a new type of analogue named as -analogue for well-known Baskakov Durrmeyer operators. considered reverse order -analogue. In this paper, we establish the direct approximation theorem, weighted theorem followed by estimations rate convergence these operators functions polynomial growth on interval.