Approximation properties of modified Szász–Mirakyan operators in polynomial weighted space

ABOUT THE AUTHORS Prashantkumar Patel is an assistant professor at SXCA and doing the PhD in Mathematics from NIT, Surat under VNM. His area of scientific interest includes approximation theory with positive linear operators and q-calculus which is proved by his research articles. Vishnu Narayan Mishra received the PhD in Mathematics from IIT, Roorkee. His research interests are in the areas of pure and applied mathematics. He has published more than 90 research articles in reputed international journals of mathematical and engineering sciences. He is a referee and an editor of several international journals in frame of Mathematics. He guided many postgraduate and PhD students. Citations of his research contributions can be found in many books and monographs, PhD thesis and scientific journal articles. Mediha Örkcü received the PhD in Mathematics from Gazi University Institute of Science Department of Mathematics during 2007–2011. Her research interest is Approximation theory. She has published many research articles in reputed international journals of Mathematics. PUBLIC INTEREST STATEMENT In this work, we define new sequence of operators depending on a parameter. We prove that these newly defined sequence of operators are positive and linear. Using the moments of these operators, we estimate continuous signals (functions). The admissible value of the involved parameter allows us to make appropriate choice of it, in order to have better approximation. We approximate these sequence of operators in terms of the modulus of continuity and the modulus of smoothness in polynomial weighted space. Received: 03 August 2015 Accepted: 25 September 2015 Published: 29 October 2015