Sentence examples for establishing existence from inspiring English sources

The Banach contraction principle [1] may be considered as one of most powerful tools for establishing existence and uniqueness of solutions for various non linear problems.

In this paper we present new ideas in fractional calculus and we present a new approach to establishing existence to some fractional differential equations in nonreflexive Banach spaces.

Proper quasimonotonicity, as introduced by Daniilidis and Hadjisavvas [7], plays a significant role in establishing existence results for (MVI) (see [8]).

His theorem actually combines both the Banach contraction principle and the Schauder fixed point theorem, and is useful in establishing existence theorems for perturbed operator equations.

Hence, all the conditions of Corollary 2.6 are satisfied and 0 is a fixed point of T. The following example underlines the crucial role of the right-hand side of (6) in establishing existence of the fixed point.

We noticed in our study that the fixed point theorems developed in the Banach algebras (see [1 5] and the references given therein) were not always useful in establishing existence principles for the problems that we are interested in Section 4.

In today's class, students will be examining whether or not such animals are real, and examining the basis upon which scientists establish existence or rule it out.

Then a linking theorem is used to establish existence.

In this work, we establish existence results for system (1.1).

Using only the axioms, we establish existence and (perhaps more surprisingly) uniqueness of stationary monetary equilibrium.

In fact, we establish existence of the Lyapunov exponent, λ= limt→∞1tlogu t,x).