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We obtain the asymptotic equalities for the least upper bounds ofapproximations by interpolation trigonometric polynomials with the equidistantnodes $x_k^{(n-1)}=\frac{2k\pi}{2n-1},\ k\in\mathbb{Z},$ in metrics of thespaces $L_p$ on classes of $2\pi$-periodic functions, representable asconvolutions of functions $\varphi, \ \varphi\perp1,$ which belongs to the unitball of the space $L_1$, and fixed generating kernels in the case where modulesof their Fourier coefficients $\psi(k)$ satisfy the condition$\lim\limits_{k\rightarrow\infty} \psi(k+1)/\psi(k)=0.$ We obtain similarestimates on the classes of $r$-differentiable functions $W^r_1$ for thequickly increasing exponents of smoothness $r$ $(r/n\rightarrow\infty)$.

Approximation by interpolation trigonometric polynomials in metrics of the spaces $L_p$ on the classes of periodic entire functions