In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, define Kantorovich extension of the operators. For functions belonging to space Lp [0, 1] , 1 ? p < ?, obtain convergence in norm by sequence Stancu-Kantorovich operators, and give an estimate for rate via first order averaged modulus smoothness. Moreover, operators; search variation detra...

Abstract We continue to study the distribution of prime numbers p, satisfying condition $\{p^{\alpha} \} \in I \subset [0; 1)$, in arithmetic progressions. In this paper, we prove an analogue Bombieri–Vinogradov theorem for 0 < α 1/9 with level $\theta = 2/5 - (3/5) \alpha$, which improves previous result corresponding \leqslant 1/3$.

Assumed that (S,+,.) is a semiring. Semiring algebra structure as generalization of ring. A set I⊆S called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I every s in S. Based on this definition, there special condition namely prime P, when αβ∈P, then could prove α or β are elements P. Furthermore, I irreducible Ia intersection from B S, I=A I=B. We also know the strongly no...