Sentence examples for convergence sequence from inspiring English sources
Let be a nonempty closed convex subset of a real Hilbert space and let be a sequence of -Lipschitzian mappings from into itself with. is said to satisfy the (SU) condition, if the following conditions hold: (1)for any strong convergence sequence, the sequence is also strong convergent; (2 the common fixed points set is nonempty; (3), where is defined by, for all, denotes the fixed points set of.
These imply that and are Cauchy sequence in, since is a convergence sequence.
Remark 4.2 Theorem 3.1 provides a convergence sequence to a common fixed point of two Lipschitzian pseudocontractive mappings, whereas Theorem 3.2 provides a convergence sequence to a common fixed point of a finite family of Lipschitzian pseudocontractive mappings.
In addition, Corollary 3.4 provides a convergence sequence to a common zero of two Lipschitzian monotone mappings, whereas Theorem 3.5 provides a convergence sequence to a common zero of a finite family of Lipschitzian monotone mappings.
By the completeness of W 1, p [ 0, 1 ], one has that ( x n ) n ∈ N is a convergence sequence.
According to Lemma 2.9 and the uniqueness of a limit of a convergence sequence, we only let (2.32).
Further, convergence rates of the convergence sequences are also proved in real Banach spaces.
The convergence domain of an infinite matrix will be denoted by and is defined by, where denotes the space of convergence sequences,.
To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure.
Convergence, Cauchy sequence and completeness in b-metric space are defined as follows.
