This paper constructs Lupaș type Bernstein operators, showing their interpolation capabilities on curved sides.
The motive of this paper is to construct Lupa{s} type Bernstein operators (B^x₁r,qF)(x₁,x₂), (B^x₂s,qF)(x₁,x₂), their products (Prs,qF)(x₁,x₂) and (Qsr,qF)(x₁,x₂) and their Boolean sums (Srs,qF)(x₁,x₂) and (Tsr,qF)(x₁,x₂) on square Dₕ with two curved side. Which interpolate a given function on the some edges and at the vertices of square. The remainders from the approximation formulas are computed using Peano's theorem.
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Arif et al. (2025) studied this question.
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