Local and global results for modified Sz\'{a}sz - Mirakjan operators

TL;DR

This paper investigates a modification of Szász-Mirakjan operators, demonstrating that many known local and global properties still hold, and confirms the generalization's significance through examples and visualizations.

Contribution

It introduces a natural modification of Szász-Mirakjan operators and shows that established properties extend to this new version, validating its relevance.

Findings

Properties of original operators are preserved in the modification.

The generalization is meaningful, supported by examples and graphical evidence.

Both local and global results remain valid for the modified operators.

Abstract

In this paper, we study a natural modification of Sz\'{a}sz - Mirakjan operators. It is shown by discussing many important established results for Sz\'{a}sz - Mirakjan operators. The results do hold for this modification as well, be they local in nature or global, be they qualitative or quantitative. It is also shown that this generalization is meaningful by means of examples and graphical representations.