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Journal of Inequalities and Applications
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Approximation in quantum calculus of the Phillips operators by using the sequences of q-Appell polynomials

Approximation in quantum calculus of the Phillips operators by using the sequences of \(q\)-Appell polynomials
Authors: Md. Nasiruzzaman; Mohammad Dilshad; S. A. Mohiuddine; Bader Mufadhi Eid Albalawi; Mohammad Rehan Ajmal;

Approximation in quantum calculus of the Phillips operators by using the sequences of q-Appell polynomials

Abstract

Abstract In this paper, we attempt to use the Dunkl analog to study the convergence properties of q-Phillips operators by using the q-Appell polynomials. By applying the new sequences of continuous functions ν s , q ( z ) = ( z − 1 2 [ s ] q ) ϱ $\nu _{s,q}(z)=\Bigl(z- \frac{1}{2[s]_{q}}\Bigr)_{\varrho}$ on [ 0 , ∞ ) $[0, \infty )$ , we construct an improved version of the q-Phillips operators. We calculate the qualitative outcomes in weighted Korovkin spaces to better understand the Phillips operators’ uniform convergence results. We obtain the approximation properties by use of the modulus of continuity and functions belonging to the Lipschitz class. Moreover, we give some direct theorems for the function belonging to Peetre’s K-functional.

Keywords

Dunkl analog, Exponential function via Dunkl analog, Approximation by positive operators, Rate of convergence, degree of approximation, exponential function via Dunkl analog, Szász operator, Generating functions, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), order of convergence, Modulus of continuity, generating functions, modulus of continuity, QA1-939, Korovkin and weighted Korovkin spaces, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
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