Sentence examples for main theorem to from inspiring English sources

We conclude with partial results on the extension of our main theorem to higher dimensions.

We now consider the applications of our main theorem to the special means.

Moreover, we apply the main theorem to a class of Hammerstein integral equations.

In this section, we apply our main theorem to prove strong convergence theorems involving equilibrium problem, variational inequality problem and fixed point problem.

We applied our main theorem to several equations and exhibited that our result improves the ones for blow-up published in the literature.

Applying the second main theorem to H : = h n ( z ) h m ( z + 1 ) and noting the equation above, we obtain.

Then, by using a scalarization method, we extend our main theorems to cone metric spaces.

Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Since then, Dhompongsa et al.[3] extended Suzuki's main theorems to a wider class of Banach spaces.

While Nieto and Rodŕiguez-López [9] studied some contractive mapping theorems in partially ordered set and applied their main theorems to obtain a unique solution for a first order ordinary differential equation.

While Nieto and López [2] extended the result of Ran and Reurings and applied their main theorems to obtain a unique solution for a first-order ordinary differential equation with periodic boundary conditions.