Sentence examples for proved a number of from inspiring English sources

Then they proved a number of fixed point theorems on these new spaces for certain type of contractions.

Elaydi and Hájek introduced the concept of exponential trichotomy for linear and nonlinear differential systems and proved a number of notable properties in these cases (see [1, 2]).

In 2008, Kirk and Panyanak [25] specialized Lim's concept to C A T ( 0 ) spaces and proved a number of results involving weak convergence in Banach spaces.

For real polynomials utilizing the Bernstein-Lorentz representation as convex combinations of fundamental polynomials, G. Lorentz, T. Erdélyi, and J. Szabados proved a number of improved versions of Schur- (and also Bernstein- and Markov-) type inequalities.

Recently, Karapinar et al. [25] have proved a number of quadruple fixed point theorems under ϕ-contractive conditions for a mapping F : X 4 → X in ordered metric spaces.

Zalmai [1] introduced some multiparameter generalizations of the class of V-r-invex functions defined by Antczak [2], and then, using the new functions, proved a number of parametric sufficient efficiency results under various Hanson-Antczak types generalized ((alpha,beta,gamma,xi,rho,theta))-V-invexity assumpthensemiinfinitemultiobjectivetiobjective fractional programming problems.

The government said in court documents it would prove a number of factors that would justify a death sentence, saying Roof had planned the killing and showed a lack of remorse.

Mr. Gore's team has based its case on a provision in the law that overturns the election if the challenger can prove "a number of illegal votes or rejection of a number of legal votes sufficient to change or place in doubt the result of the election".

Although the inclusion of California, the most populous state, with one of the biggest economies in the world, and New York, the financial capital, might surprise some people, other poverty experts said the poverty line could be statistically manipulated to prove a number of points.

They then prove a number of theorems, which generalizes a result proved by Ehlers and Köhler (1977).

En route, we prove a number of moment and cumulant estimates for R-diagonal elements that are of independent interest.