A note on a general sequence of $$\lambda $$-Szász Kantorovich type operators

Rao, Nadeem; Ayman-Mursaleen, Mohammad; Aslan, Reşat

doi:10.1007/s40314-024-02946-6

Comp. Appl. Math.

2024

DOI: 10.1007/s40314-024-02946-6

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A note on a general sequence of $$\lambda $$-Szász Kantorovich type operators

Nadeem Rao,

Mohammad Ayman-Mursaleen,

Reşat Aslan

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Cited by 5 publications

References 32 publications

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Some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of $$\alpha$$

Aslan

2024

Iran J Sci

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Some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of $$\alpha$$

Aslan

2024

Iran J Sci

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Weighted Statistical Convergence and Cluster Points: The Fibonacci Sequence-Based Approach Using Modulus Functions

Ibrahim,

Brevik,

Agarwal

et al. 2024

Mathematics

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In this paper, the Fibonacci sequence, renowned for its significance across various fields, its ability to illuminate numerical concepts, and its role in uncovering patterns in mathematics and nature, forms the foundation of this research. This study introduces innovative concepts of weighted density, weighted statistical summability, weighted statistical convergence, and weighted statistical Cauchy, uniquely defined via the Fibonacci sequence and modulus functions. Key theorems, relationships, examples, and properties substantiate these novel principles, advancing our comprehension of sequence behavior. Additionally, we extend the notion of statistical cluster points within a broader framework, surpassing traditional definitions and offering deeper insights into convergence in a statistical context. Our findings in this paper open avenues for new applications and further exploration in various mathematical fields.

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Summed Series Involving 1F2 Hypergeometric Functions

Straton

2024

Mathematics

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Summation of infinite series has played a significant role in a broad range of problems in the physical sciences and is of interest in a purely mathematical context. In a prior paper, we found that the Fourier–Legendre series of a Bessel function of the first kind JNkx and modified Bessel functions of the first kind INkx lead to an infinite set of series involving 1F2 hypergeometric functions (extracted therefrom) that could be summed, having values that are inverse powers of the eight primes 1/(2i3j5k7l11m13n17o19p) multiplying powers of the coefficient k, for the first 22 terms in each series. The present paper shows how to generate additional, doubly infinite summed series involving 1F2 hypergeometric functions from Chebyshev polynomial expansions of Bessel functions, and trebly infinite sets of summed series involving 1F2 hypergeometric functions from Gegenbauer polynomial expansions of Bessel functions. That the parameters in these new cases can be varied at will significantly expands the landscape of applications for which they could provide a solution.

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A note on a general sequence of $$\lambda $$-Szász Kantorovich type operators

Cited by 5 publications

References 32 publications

Some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of $$\alpha$$

Some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of $$\alpha$$

Weighted Statistical Convergence and Cluster Points: The Fibonacci Sequence-Based Approach Using Modulus Functions

Summed Series Involving 1F2 Hypergeometric Functions

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