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In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural deduction s
In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Morticis lemma.
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We derive the q-an
We study the two-weighted estimate [ bigg|sum_{k=0}^na_k(x)int_0^xt^kf(t)dt|L_{q,v}(0,infty)bigg|leq c|f|L_{p,u}(0,infty)|,tag{$*$} ] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<pleq qleqinfty$, prov
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold.