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Generalized [Formula: see text]-Bleimann-Butzer-Hahn operators and some approximation results
M Mursaleen1,2, Md Nasiruzzaman3, Khursheed J Ansari4
1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Journal of Inequalities and Applications
|January 2, 2018
Summary
This study introduces novel [Formula: see text]-integer-based generalizations of Bleimann-Butzer-Hahn operators. These new operators demonstrate promising approximation results and shape-preserving properties in mathematical analysis.
Area of Science:
- Mathematical Analysis
- Approximation Theory
Background:
- Bleimann-Butzer-Hahn operators are fundamental in approximation theory.
- Generalizations of these operators are crucial for expanding their applicability.
- The use of [Formula: see text]-integers offers a novel approach to operator construction.
Purpose of the Study:
- To introduce a new class of generalized Bleimann-Butzer-Hahn operators.
- To utilize [Formula: see text]-integers and a continuously differentiable function μ for operator definition.
- To analyze the approximation and shape-preserving characteristics of these novel operators.
Main Methods:
- Construction of generalized operators using [Formula: see text]-integers.
- Application of Korovkin-type theorems to establish approximation results.
- Computation of the degree of approximation via the modulus of continuity.
- Investigation of shape-preserving properties.
Main Results:
- Establishment of Korovkin-type approximation theorems for the new operators.
- Quantitative estimation of the degree of approximation.
- Demonstration of shape-preserving capabilities of the introduced operators.
- The new operators offer enhanced approximation properties.
Conclusions:
- The introduced generalization of Bleimann-Butzer-Hahn operators is effective.
- The operators possess significant approximation and shape-preserving properties.
- This work contributes to the field of approximation theory with novel operator constructions.
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