Two New Bailey Lattices and Their Applications

Jia, Zeya; Khan, Bilal; Agarwal, Praveen; Hu, Qiuxia; Wang, Xinjing

doi:10.3390/sym13060958

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…For some other applications in the related area, we refer readers to previous works. [20][21][22][23][24][25] Motivated from the real case and overconvergence properties of above work on complex operators, we consider the complex form of the operators (1.2), for n ∈ N, 𝛼 ∈ [0, 1], z ∈ C and 𝑓 ∶ [0, 1] → C, a complex valued analytic function as follows:…”

Section: Introductionmentioning

confidence: 99%

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Approximation properties of complex genuine α–Bernstein‐Durrmeyer operators

Goyal

2022

Math Methods in App Sciences

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Herein, we propose a complex form of genuine Bernstein‐Durrmeyer type operators depending on a non‐negative real parameter α$$ \alpha $$. We present the quantitative upper bound, Voronovskaja type result and the exact order of approximation for the derivatives of the operators attached to analytic functions on compact disks. These results validate the extension of approximation properties of complex genuine α$$ \alpha $$–Bernstein‐Durrmeyer type operators from real intervals to compact disks in the complex plane.

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Section: Introductionmentioning

confidence: 99%

“…Several types of complex operators were studied by a number of authors (see literature 10–19 ). For some other applications in the related area, we refer readers to previous works 20–25 …”

Section: Introductionmentioning

confidence: 99%

Approximation properties of complex genuine α–Bernstein‐Durrmeyer operators

Goyal

2022

Math Methods in App Sciences

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“…Particularly, in the Theory of Partitions, Quantum Mechanics, Lie Theory, Mechanical Engineering, Combinatorial Analysis, Theory of Heat Conduction, Cosmology, Non-Linear Electric Circuit Theory, Particle Physics, Finite Vector Spaces and Statistics (see, for example, [7] (pp. 350, 351); see also [8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Applications of Generalized q-Difference Equations for General q-Polynomials

Jia

Khan

et al. 2021

Symmetry

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Andrews gave a remarkable interpretation of the Rogers–Ramanujan identities with the polynomials ρe(N,y,x,q), and it was noted that ρe(∞,−1,1,q) is the generation of the fifth-order mock theta functions. In the present investigation, several interesting types of generating functions for this q-polynomial using q-difference equations is deduced. Besides that, a generalization of Andrew’s result in form of a multilinear generating function for q-polynomials is also given. Moreover, we build a transformation identity involving the q-polynomials and Bailey transformation. As an application, we give some new Hecke-type identities. We observe that most of the parameters involved in our results are symmetric to each other. Our results are shown to be connected with several earlier works related to the field of our present investigation.

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“…In addition, Jia et al [6] developed two new Bailey lattices and defined a number of new-form q-multisums with multiple variables for the basic hypergeometric series, which arose as consequences of these two new Bailey lattices. As applications, they derived two new transformations for basic hypergeometry using the unit Bailey pair.…”

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confidence: 99%