Geodesic
Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters
Filomat, Tome 36 (2022) no. 4, p. 1179

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Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich operators generated by the basic q-calculus. More precisely, we study the convergence properties of our new operators in the space of continuous functions and Lebesgue space. We obtain the degree of convergence with the help of modulus of continuity and integral modulus of continuity. Furthermore, we establish the quantitative estimates of Voronovskaja-type
DOI : 10.2298/FIL2204179A
Classification : 41A36, 441A25, 33C45
Keywords: Bernstein-Stancu type polynomials, q-calculus, modulus of continuity, Peetre’s K-functional, Korovkin’s theorem, Voronovskaja-type theorem 
Mohammad Ayman Mursaleen; Adem Kilicman; Md Nasiruzzaman. Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters. Filomat, Tome 36 (2022) no. 4, p. 1179 . doi: 10.2298/FIL2204179A
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     author = {Mohammad Ayman Mursaleen and Adem Kilicman and Md Nasiruzzaman},
     title = {Approximation by {q-Bernstein-Stancu-Kantorovich} operators with shifted knots of real parameters},
     journal = {Filomat},
     pages = {1179 },
     year = {2022},
     volume = {36},
     number = {4},
     doi = {10.2298/FIL2204179A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2204179A/}
}
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