Abstract
In this article, we construct a generalized Kantorovich operator based on Hermite polynomials of three variable to approximate integrable functions. For the operator, we derive the moment generating function (m.g.f.) and a few direct findings associated with m.g.f. We continue by examining the quantitative asymptotic formula and convergence in relation to the modulus of continuity and pace at which our operator converges has shown graphically. Then we capture new discrete type operator based on composition of operators and studied its local convergence and a Voronovskaja theorem in weighted space and some direct results.
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Gupta, V., Malik, D. On a new Kantorovich operator based on Hermite polynomials. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02068-6
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DOI: https://doi.org/10.1007/s12190-024-02068-6
Keywords
- Kantorovich
- Linear positive operator
- Modulus of continuity
- Asymptotic formula
- Moment generating function
- Convergence estimates
- Hermite polynomials