Sentence examples for an implicit relation from inspiring English sources

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.

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

In Sections 2-3, we first introduce the new real function class A φ satisfying an implicit relation.

We denote by A φ the collection of all real functions F : R 4 + → R satisfying an implicit relation.

Our aim in this paper is to introduce a generalization of f-contractiveness through an implicit relation.

The existence and (under additional assumptions) uniqueness of their common fixed point is obtained under assumptions that these mappings are strictly weakly isotone increasing, one is orbitally continuous and they satisfy a implicit relation condition.

Assume that T : A → B is a continuous implicit relation type modified α 3 -proximal contraction such that the following conditions hold: (i) T is an α 3 -proximal admissible mapping and T ( A 0 ) ⊆ B 0,   (ii) there exist x 0, x 1 ∈ A 0 such that d ( x 1, T x 0 ) = d ( A, B ), α ( x 0, x 1 ) ≥ 1, α ( x 0, x 0 ) ≥ 1 and α ( x 1, x 1 ) ≥ 1.  .

The parser determines that a RESTATEMENT implicit relation exists between the two sentences.

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].

Beg and Butt [19] studied set-valued mappings and proved common fixed point results for mappings satisfying implicit relation in a partially ordered metric space.