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On preservation of functions with exponential growth by certain Exponential operators
  • Nav Mishra,
  • Naokant Deo
Nav Mishra
Delhi Technological University
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Naokant Deo
Delhi Technological University
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Abstract

In this study, our aim is to provide a modification of the so-called Ismail-May operators that preserve exponential functions \(e^{Ax},A\in\mathbb{R}\). In consonance to this, we begin with estimating the convergence rate of the operators in terms of usual and exponential modulus of continuity. We also provide a global approximation and a quantitative Voronovskaya result. Moreover, to validate the modification, we exhibit some graphical representations using Mathematica software to compare the original operator and its modification. We conclude that the modified operators not only preserve exponential functions but also provide faster rate of convergence when \(A>0\).

Peer review status:ACCEPTED

16 May 2020Submitted to Mathematical Methods in the Applied Sciences
23 May 2020Submission Checks Completed
23 May 2020Assigned to Editor
15 Jul 2020Reviewer(s) Assigned
05 Nov 2020Review(s) Completed, Editorial Evaluation Pending
30 Dec 2020Editorial Decision: Revise Major
10 Jan 20211st Revision Received
11 Jan 2021Assigned to Editor
11 Jan 2021Submission Checks Completed
16 Jan 2021Reviewer(s) Assigned
16 Jan 2021Review(s) Completed, Editorial Evaluation Pending
17 Jan 2021Editorial Decision: Revise Major
18 Jan 20212nd Revision Received
18 Jan 2021Submission Checks Completed
18 Jan 2021Assigned to Editor
21 Jan 2021Reviewer(s) Assigned
05 Feb 2021Review(s) Completed, Editorial Evaluation Pending
05 Feb 2021Editorial Decision: Revise Minor
08 Feb 20213rd Revision Received
08 Feb 2021Assigned to Editor
08 Feb 2021Submission Checks Completed
08 Feb 2021Editorial Decision: Accept