Sentence examples for midpoint map and from inspiring English sources

Let X be complete geodesic Ptolemy space with a uniformly continuous midpoint map and T be a mapping.

Theorem 2.21 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, and K ⊆ X nonempty, bounded, closed, and convex.

Theorem 3.1 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, and suppose that K ⊆ X is nonempty, bounded, closed, and convex.

If A ( { x n } ) = y, then y is a fixed point of T. Theorem 3.12 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, and K ⊆ X nonempty, bounded, closed, and convex.

Theorem 2.13 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, and K be a nonempty bounded, closed, and convex subset of X. Suppose T : K → P c l, b d ( K ) is a multi-valued mapping satisfying E ′ and C λ ′ conditions, then F ( T ) ≠ ∅.

Theorem 2.2 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, and K a nonempty bounded, closed, and convex subset of X. Suppose T : K → P c p ( K ) is a multi-valued mapping satisfying the C condition, then F ( T ) ≠ ∅.

Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, { x n } ⊆ X a bounded sequence and K ⊆ X is nonempty, closed, and convex.

Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, { x n } ⊆ X a bounded sequence and K ⊆ X nonempty closed and convex.

Theorem 3.2 Let K be a nonempty closed, convex, and bounded subset of a complete geodesic Ptolemy space with a uniformly continuous midpoint map X. Suppose that T : K → K satisfies the conditions E and C λ for some λ ∈ ( 0, 1 ).

They prove that a geodesic Ptolemy space with a uniformly continuous midpoint map is reflexive.

Espinola and Nicolae in [5] proved a geodesic Ptolemy space with a uniformly continuous midpoint map is reflexive.