The equivalence between Mann and implicit Mann iterations

The Equivalence between Mann and Implicit Mann Iterations

We shall prove the equivalence bewteen the convergences of Mann and implicit Mann iterations dealing with various classes of non-Lipschitzian operators.

On Equivalence between Convergence of Ishikawa––mann and Noor Iterations

In this paper, we prove the equivalence of convergence between the Mann–Ishikawa– Noor and multistep iterations for Φ− strongly pseudocontractive and Φ− strongly accretive type operators in an arbitrary Banach spaces. Results proved in this paper represent an extension and refinement of the previously known results in this area. Mathematics subject classification (2010): 47H09, 47H10, 47H15.

Implicit Mann fixed point iterations for pseudo-contractive mappings

Let K be a compact convex subset of a real Hilbert space H and T:K→K a continuous hemicontractive map. Let {an},{bn} and {cn} be real sequences in [0, 1] such that an+bn+cn=1, and {un} and {vn} be sequences in K. In this paper we prove that, if {bn}, {cn} and {vn} satisfy some appropriate conditions, then for arbitrary x0K, the sequence {xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1, conv...

The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions

The Equivalence between T-Stabilities of The Krasnoselskij and The Mann Iterations

Let X be a normed space and T a selfmap of X . Let x0 be a point of X , and assume that xn+1 = f (T ,xn) is an iteration procedure, involving T , which yields a sequence {xn} of points from X . Suppose {xn} converges to a fixed point x∗ of T . Let {ξn} be an arbitrary sequence in X , and set n = ‖ξn+1− f (T ,ξn)‖ for all n∈N. Definition 1.1 [1]. If (limn→∞ n = 0) ⇒ (limn→∞ ξn = p), then the ite...