Sentence examples for be a generalized multivalued from inspiring English sources

Let be a generalized multivalued almost -contraction and let and be such that (2.12).

(3) Let (X, d) be a metric space and T : X → C B ( X ) be a generalized multivalued (φ, L -weak contraction [11], that is, there exists an M T -function φ and L -weakucontraction T x, T y ) ≤ φ ( d ( x, y ) ) d ( x, y ) + L d ( y, T x ) for all x, y ∈ X.  .

A mapping T : X → A ˜ is said to be a generalized multivalued contraction if and only if there exists λ ∈ [ 0, 1 ) such that, for all x, y ∈ X, H ( T x, T y ) ≤ λ ⋅ max { d ( x, y ), d ( x, T x ), d ( y, T y ), d ( x, T y ) + d ( y, T x ) 2 }, (1.4). where H ( A, B ) for A, B ∈ A ˜ is the Hausdorff metric (1.2) induced by metric d.

Suppose that a mapping T : X → A ˜ is a generalized multivalued contraction defined in Definition 1.12.

We say that is a generalized multivalued almost -contraction if there exists a function satisfying for every such that (2.9).

If is a generalized multivalued almost contraction, then has a fixed point provided either is compact and the function is lower semicontinuous or is closed and compact.

Definition 2.16 Let ( X, d ) be a generalized metric space, and let F : X → P ( X ) be a multivalued operator.

Definition 2.12 Let ( X, d ) be a generalized metric space, and let F : X → P cl ( X ) be a multivalued operator.

Theorem 2.19 Let ( X, d ) be a generalized metric space, and let F : X → P cl ( X ) be a multivalued ψ-weakly Picard operator.

Corollary 2.20 Let ( X, d ) be a generalized complete metric space, and let F : X → P cl ( X ) be a multivalued A-contraction with proximinal values.

Let be an arbitrary metric space and a generalized multivalued almost contraction.