Sentence examples for basic theorems in the from inspiring English sources

This study is dedicated to some basic theorems in the thermoelastodynamics of microstretch bodies.

The basic theorems in the theory have many applications to various equilibrium problems in nonlinear analysis and other fields.

They gave the version of the Banach contraction principle and other basic theorems in the setting of cone metric spaces.

Moreover, refined versions of the basic theorems in the KKM theory for abstract convex spaces are given in a recent study of Park [47].  .

In 2007, Huang and Zhang [1] introduced the concept of cone metric spaces, as a generalization of metric spaces, and gave the version of the Banach contraction principle and other basic theorems in the setting of cone metric spaces.

Consequently, at the beginning, the basic theorems in the KKM theory and their applications were established for convex subsets of topological vector spaces mainly by Fan in 1961-84 [5–11].

His best-known work concerned the analytic representation of a single-valued function; this work culminated in the Mittag-Leffler theorem, one of the basic theorems in analytic function theory.

Motivated by [8], our purpose is to apply some basic theorems in topological degree theory and fixed point index theory to establish some conditions for the nonlinear function f, which are able to guarantee the existence of sign-changing solutions, positive solutions, and negative solutions for the above discrete boundary value problem.

By making use of a basic theorem in mathematical statistics concerning unbiased estimators with minimum variance, Gurland [15] presented the following inequality: [ Γ ( ( n + 1 ) / 2 ) Γ ( n / 2 ) ] 2 < n 2 2 n + 1 (14).

One basic theorem in quality improvement is that change is a prerequisite for improvement to happen but that every change does not guarantee improvement.

Based on a basic theorem in mathematical statistics concerning unbiased estimators with minimum variance, Gurland [1] yielded a closer approximation to π than that afforded by (1.1), namely, begin{aligned} frac{4n+3}{(2n+1)^{2}} biggl( frac{(2n)!!}{(2n-1)!!} biggr)^{2}< pi< frac {4}{4n+1} biggl( frac{(2n)!!}{(2n-1)!!} biggr)^{2}, quad n in mathbb{N}.