Abstract
In this paper, we study Gupta type family of positive linear operators,
which have a wide range of many well known linear positive operators
e.g. Phillips, Baskakov-Durrmeyer, Baskakov-Sz\’{a}sz,
Sz\’{a}sz-Beta, Lupa\c{s}-Beta,
Lupa\c{s}-Sz\’{a}sz, genuine
Bernstein-Durrmeyer, Link,
P\u{a}lt\u{a}nea,
Mihe\c{s}an-Durrmeyer, link Bernstein-Durrmeyer etc. We
first establish direct results in terms of usual modulus of continuity
having order 2 and Ditzian-Totik modulus of smoothness and then study
quantitative Voronovkaya theorem for the weighted spaces of functions.
Further, we establish Gr\“{u}ss-Voronovskaja type
approximation theorem and also derive
Gr\”{u}ss-Voronovskaja type asymptotic result in
quantitative form.