Q-Analogue of Generalized Bernstein–Kantorovich Operators

On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽

10.3390/math9111235 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1235

Author(s):

Bianca Ioana Vasian ◽

Ștefan Lucian Garoiu ◽

Cristina Maria Păcurar

Keyword(s):

Test Functions ◽

New Class ◽

Convergence Results ◽

Error Estimations ◽

Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

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Quantitative Estimates for Nonlinear Sampling Kantorovich Operators

Results in Mathematics ◽

10.1007/s00025-021-01383-9 ◽

2021 ◽

Vol 76 (2) ◽

Author(s):

Nursel Çetin ◽

Danilo Costarelli ◽

Gianluca Vinti

Keyword(s):

Orlicz Spaces ◽

General Setting ◽

Modulus Of Smoothness ◽

Direct Approach ◽

Order Of Approximation ◽

Lipschitz Classes ◽

General Frame ◽

Quantitative Estimates ◽

Nonlinear Sampling ◽

Kantorovich Operators

AbstractIn this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $$L^{p}$$ L p -spaces, $$1\le p<\infty $$ 1 ≤ p < ∞ , and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the $$L^p$$ L p -case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.

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The family of Bernstein–Kantorovich operators with shifted knots

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-021-00677-9 ◽

2021 ◽

Author(s):

Ram Pratap ◽

Naokant Deo

Keyword(s):

The Family ◽

Kantorovich Operators

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The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

Carpathian Journal of Mathematics ◽

10.37193/cjm.2018.03.11 ◽

2018 ◽

Vol 34 (3) ◽

pp. 363-370

Author(s):

M. MURSALEEN ◽

◽

MOHD. AHASAN ◽

Keyword(s):

Rate Of Convergence ◽

Modulus Of Continuity ◽

Exponential Function ◽

Second Order ◽

Lipschitz Functions ◽

Linear Operators ◽

Positive Linear Operators ◽

Approximation Properties ◽

Kantorovich Operators ◽

Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

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