Sentence examples for be a complete multiplicative from inspiring English sources

Let ((X, d)) be a complete multiplicative metric space, T be a mapping of X into itself.

Let ( X, d ) be a complete multiplicative metric space and f : X → X be a multiplicative Chatterjea-contraction mapping.

Let ((X, d)) be a complete multiplicative metric space, S be a mapping of X into itself.

Let ((X, d)) be a complete multiplicative metric space, S and T be two mappings of X into itself.

Let ( X, d ) be a complete multiplicative metric space and f : X → X be a multiplicative Kannan-contraction mapping.

Theorem 2.11 Let ( X, d ) be a complete multiplicative metric space and f : X → X be a multiplicative -Chatterjea-contraction mapping.

Clearly, ( X, d ) is a complete multiplicative metric space.

It is easy to see that ( X, d ∗ ) is a complete multiplicative metric space.

A mapping f : A ∪ B → A ∪ B is called cyclic if f ( A ) ⊆ B and f ( B ) ⊆ A. Theorem 3.4 Let A and B be two closed subsets of a complete multiplicative metric space ( X, d ) such that A ∩ B ≠ ∅ and f : A ∪ B → A ∪ B be a cyclic mapping.

Theorem 3.5 Let A and B be two closed subsets of a complete multiplicative metric space ( X, d ) such that A ∩ B ≠ ∅ and f : A ∪ B → A ∪ B be a cyclic mapping.

Then f has a unique fixed point in A ∩ B. Theorem 3.6 Let A and B be two closed subsets of a complete multiplicative metric space ( X, d ) such that A ∩ B ≠ ∅ and f : A ∪ B → A ∪ B be a cyclic mapping.