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A kind of Abel–Goncharov type operators is surveyed. The presented method is studied by combining the known multiquadric quasi-interpolant with univariate Abel–Goncharov interpolation polynomials. The construction of new quasi-interpolants  ℒ m AG f has the property of  m m ∈ ℤ , m &gt; 0 degree polynomial reproducing and converges up to a rate of  m + 1 . In this study, some error bounds and convergence rates of the combined operators are studied. Error estimates indicate that our operators could provide the desired precision by choosing the suitable shape-preserving parameter c and a nonnegative integer m. Several numerical comparisons are carried out to verify a higher degree of accuracy based on the obtained scheme. Furthermore, the advantage of our method is that the associated algorithm is very simple and easy to implement.

Abel–Goncharov Type Multiquadric Quasi-Interpolation Operators with Higher Approximation Order