Sentence examples for give refinements from inspiring English sources

Further, we give refinements of Theorems 1.2, 1.4, and 1.5.

In this paper, we will give refinements of (1.6) and (1.7) in Section 2.

The purpose of this paper is to give refinements of (1.5) and (1.6).

In this paper, we give refinements of some inequalities for generalized monotone functions by using log-convexity of some functionals.

We give refinements of Hermite-Hadamard type inequalities for convex functions of self-adjoint operators in a Hilbert space analogous to well-known inequalities of the same type.

In [2], Alomari et al. established Hermite-Hadamard-type inequalities for quasi-convex functions which give refinements of those given above in Theorem 4 and Theorem 5.

THE French may have given refinement to ice cream with their coupes and parfaits, but it took American excess and ingenuity to create the sundae -- as messy and irresistible as democracy itself.

In Remark 5, we show that the assumption of convexity gives refinement to the inequality in Theorem 4.

Patch or grid based AMR often employs ghost cells to decouple the hyperbolic advances of each grid on a given refinement level.

In [6], a refinement of Bellman's inequality is given for positive integer ; here, we give further refinements of Bellman's inequality for real.

The purpose of this paper is to give some refinements of the classical Jensen's inequality.