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On [Formula: see text]-Szász-Mirakyan operators and their approximation properties
M Mursaleen1,2, Aah Al-Abied1, Abdullah Alotaibi2
1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Journal of Inequalities and Applications
|September 15, 2017
Summary
This study introduces modified Szász-Mirakyan operators using q-integers, exploring their approximation capabilities. The research establishes weighted approximation and a Voronovskaya-type theorem for these novel operators.
Area of Science:
- Mathematical Analysis
- Approximation Theory
Background:
- Szász-Mirakyan operators are fundamental in approximation theory.
- Investigating modifications of classical operators can lead to improved approximation properties.
Purpose of the Study:
- Introduce a novel modification of Szász-Mirakyan operators.
- Analyze the approximation properties of these new operators.
- Establish theoretical results regarding their convergence and behavior.
Main Methods:
- Construction of new Szász-Mirakyan operators based on q-integers.
- Application of techniques from approximation theory to analyze operator convergence.
- Derivation of weighted approximation results.
- Formulation and proof of a Voronovskaya-type theorem.
Main Results:
- A new class of Szász-Mirakyan operators utilizing q-integers has been successfully defined.
- The weighted approximation properties of these operators have been rigorously investigated.
- A Voronovskaya-type theorem has been established for the newly introduced operators, providing insights into their local behavior.
Conclusions:
- The modified Szász-Mirakyan operators offer a new tool for approximation.
- The q-integer modification enhances the theoretical understanding of these operators.
- The established theorems provide a foundation for further research in this area.
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