Sentence examples for functional fixed from inspiring English sources

Prasad and Krushna [8] studied FOBVPs with p-Laplacian operator with the help of the Krasnosel'skii and five functional fixed point theorems and checked their results by examples.

Building upon these basic premises, modifications of the MKT allow for the quantification of the proportion of functional fixed differences that are adaptive and the rate at which these new adaptive mutations appear (Smith and Eyre-Walker 2002; Eyre-Walker 2006; Fay 2011).

The well-known Avery-Henderson fixed point theorem and the five functionals fixed point theorem are adopted in the arguments.

Thus, we set out to verify that the operator T satisfies four functionals fixed point theorem, which will prove the existence of a fixed point of T. We first show that Q ( α, β, r, R ) is bounded, and T : Q ( α, β, r, R ) → P is completely continuous.

Thus we set out to verify that the operator T satisfies four functionals fixed point theorem, which will prove the existence of a fixed point of T. We first show that Q ( α, β, r, R ) is bounded and T : Q ( α, β, r, R ) → K is completely continuous.

Lemma 2.3 (four functionals fixed point theorem).

We are now in a position to present the Five functionals fixed point theorem (see [17]).

By using the Four functionals fixed point theorem and Five functionals fixed point theorem, we obtain the existence criteria of at least one positive solution and three positive solutions for the BVP (1.3).

By using the four functionals fixed point theorem and five functionals fixed point theorem, they obtained the existence criteria of at least one positive solution and three positive solutions.

The first one is based on the Four functionals fixed point theorem in the work of R. Avery et al. (2008), and the second one is based on the Five functionals fixed point theorem.

By using the five functionals fixed point theorem [20], Liu obtained the existence criteria of at least three positive solutions.