q-Cesáro Rational Fourier–Chebyshev Integral Operators and Their Approximation Properties

Approximation properties of q -Cesáro sums of rational Fourier–Chebyshev integral operators with arbitrary fixed number of geometrically different poles are studied. For this method of rational approximation, an integral representation is obtained. The suprema of the q -Cesáro sums of the polynomial Fourier–Chebyshev series are evaluated on classes of γ -Hölder functions with γ ∈ (0,1] on $$[-1,1]$$ . Approximations of the function |x|ˢ , s ∈ (0,2) , on $$[-1,1]$$ by the rational q -Cesáro sums are studied. An asymptotic expression of the majorant of uniform approximations depending on the parameters of an approximated function functions is derived, and the values of these parameters are given for which the majorant converges to zero most rapidly. For s ∈ (0,1] , the uniform rational approximation by our method are shown to have a greater decrease rate in comparison with their polynomial analogues.