Geodesic
Approximation by λ-Bernstein type operators on triangular domain
Filomat, Tome 37 (2023) no. 6, p. 1941

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DOI

In this paper, a new type of λ-Bernstein operators (B w m,λ) (w, z) and (B z n,λ) (w, z), their Products (P mn,λg) (w, z), (Q nm,λ) (w, z), and their Boolean sums (S mn,λ) (w, z), (T nm,λ) (w, z) are constructed on triangle R h with parameter λ ∈ [−1, 1]. Convergence theorem for Lipschitz type continuous functions and a Voronovskaja-type asymptotic formula are studied for these operators. Remainder terms for error evaluation by using the modulus of continuity are discussed. Graphical representations are added to demonstrate the consistency of theoretical findings for the operators approximating functions on the triangular domain. Also, we show that the parameter λ will provide flexibility in approximation; in some cases, the approximation will be better than its classical analogue.
DOI : 10.2298/FIL2306941C
Classification : 41A35, 41A36, 41A80
Keywords: λ-Bernstein operators, Triangular domain, Product and Boolean sum operator, Modulus of continuity, Error evaluation 
Qing-Bo Cai; Asif Khan; Mohd Shanawaz Mansoori; Mohammad Iliyas; Khalid Khan. Approximation by λ-Bernstein type operators on triangular domain. Filomat, Tome 37 (2023) no. 6, p. 1941 . doi: 10.2298/FIL2306941C
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     author = {Qing-Bo Cai and Asif Khan and Mohd Shanawaz Mansoori and Mohammad Iliyas and Khalid Khan},
     title = {Approximation by {\ensuremath{\lambda}-Bernstein} type operators on triangular domain},
     journal = {Filomat},
     pages = {1941 },
     year = {2023},
     volume = {37},
     number = {6},
     doi = {10.2298/FIL2306941C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2306941C/}
}
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