Direct estimates for certain Szász type operators

• We deal with the modified forms of the Szász basis functions.
• We introduce a new sequence of linear positive operators of Durrmeyer type.
• Direct estimates for the new sequence have been discussed.
• An open problem is also proposed.

The present paper deals with the modified forms of the Szász basis functions. We propose a Durrmeyer type operator having the basis functions in summation and integration due to Jain (1972) and Paˇltaˇnea (2008). We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation. In the end, we give an open problem for the readers.