Sentence examples for be two fixed points from inspiring English sources

For x ∈ Fix ( T ), β ( x, z, z ) ≥ 1 for all z ∈ X. Proof Let u, v ∈ Fix ( T ) be two fixed points of T. By (iv), we derive β ( u, v, v ) ≥ 1.

Let x and y be two fixed points for f.

Indeed let and be two fixed points of.

Let and be two fixed points of the map.

Let z and y be two fixed points of f.

Now suppose x, y be two fixed points of f and T.

Let (x_) and (y_) be two fixed point of f.

Definition 2.2 Let { u n } and { v n } be two fixed point iteration procedures that converge to the same fixed point p and satisfy (2.2) and (2.3), respectively.

Let ({u_{n}}_{ngeq0}) and ({v_{n}}_{ngeq0}) be two fixed point iteration procedures that converge to the same fixed point p and (|u_{n}-p|leq a_{n}) and (|v_{n}-p|leq b_{n}) for all (ngeq0).

Then S has a unique fixed point x ∗ and d q ( x ∗, x ∗ ) = 0. Assume that x ∗ and y ∗ be two fixed point of S in B ( x 0, r ) ¯, then, by assumption, α ( x ∗, y ∗ ) ≥ η ( x ∗, y ∗ ), d q ( x ∗, y ∗ ) = d q ( S x ∗, S y ∗ ) ≤ ψ ( d q ( x ∗, y ∗ ) ) A contradiction to the fact that for each t > 0, ψ ( t ) < t.

Thus, all the hypotheses of Theorem 3.2 are satisfied and T has at least a fixed point; here 0 and 2 are two fixed points of T. On the other hand, T is not a fuzzy contractive mapping of Gregori and Sapena [6].