Sentence examples for maps satisfying the from inspiring English sources

Finally, we give important examples of multi-valued maps satisfying the conditions of our theorems.

Now, let us introduce the class of maps satisfying the KKM property.

Then, under the scope of circular metric space, we present a number of fixed point theorems for maps satisfying the KKM property.

In this paper, we investigate the existence and uniqueness of fixed points of maps satisfying the C -condition on metric spaces and on partially ordered metric spaces.

The existence and uniqueness of fixed points of maps satisfying the C -condition have also been extensively studied; see [12] [14].

The main purpose of this paper is to study some topological nature of circular metric spaces and deduce some fixed point theorems for maps satisfying the KKM property.

In the following example we give a self-mapping satisfying the conditions of Theorems 2.7 and 2.9, respectively, but does not satisfy the condition of Theorem 2.4.

The self-mappings are called generalized -pair if there exist a -mapping and a mapping satisfying the conditions, and such that (2.1).

If f and g are self-maps satisfying the inequality d ( f x, g y ) ≤ α u ( x, y ) + L N ( x, y ), (2.11).

Suppose ψ : [ 0, ∞ ) → [ 0, ∞ ) is an altering distance function and φ : [ 0, ∞ ) → [ 0, ∞ ) is a lower semi-continuous function with φ ( t ) = 0 if and only if t = 0. Moreover, suppose that f and g are self-maps satisfying the inequality ψ ( d ( f x, g y ) ) ≤ ψ ( λ u ( x, y ) ) − φ ( λ u ( x, y ) ) + L N ( x, y ), (2.1).

Let be a mapping satisfying the condition.