Sentence examples for implicit relations from inspiring English sources

First, we give some implicit relations for subsequent use.

So, we take the norm ∥ u ∥ = max { ∥ u ′ ∥ 0, ∥ u ″ ∥ 0 } by finding some implicit relations.

In this paper, we prove a coupled coincidence point theorem for mappings satisfying such implicit relations.

Implicit relations have been considered by several authors in connection with solving nonlinear functional equations (see [22 25]).

Several common fixed point theorems have been proved by many researchers in framework of fuzzy metric spaces via implicit relations (see [5, 18, 23, 34]).

We present some fixed point results for nondecreasing and weakly increasing operators in a partially ordered metric space using implicit relations.

In [21], Berinde obtained some constructive fixed point theorems for almost contractions satisfying an implicit relation.

Before this, we will define an implicit relation for the contractive condition of the theorem.

Then it is easy to see that F ⊂ A φ, which implies that the implicit relation of Definition 2.5 is a generalization of Aliouche and Fisher [[13], implicit relation].

Now we give a fixed point theorem for two weakly increasing mappings in ordered metric spaces using an implicit relation.

In the Section 3, we generalized the above contractive conditions using the implicit relation technique in such a way that.