Iterative Methods for Nonlinear Lipschitz Pseudocontractive Operators

Convergence Theorems and Stability Results for Lipschitz Strongly Pseudocontractive Operators

Iterative Approximation of Fixed Points of Lipschitz Pseudocontractive Maps

Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., `p, 1 < p < ∞). Let T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K of E and let ω ∈ K be arbitrary. Then the iteration sequence {zn} defined by z0 ∈ K, zn+1 = (1 − μn+1)ω + μn+1yn; yn = (1 − αn)zn + αnTzn, converges strongly to a fixed poi...

On Convergence Results for Lipschitz Pseudocontractive Mappings

Iterative Methods for Pseudocontractive Mappings in Banach Spaces

and Applied Analysis 3 Lemma 1 (see [1, 2]). Let E be a Banach space and let J be the normalized duality mapping on E. Then for any x, y ∈ E, the following inequality holds: 󵄩󵄩󵄩󵄩x + y 󵄩󵄩󵄩󵄩 2 ≤ ‖x‖ 2 + 2⟨y, j (x + y)⟩, ∀j (x + y) ∈ J (x + y) . (14) Lemma 2 (see [20]). Let {s n } be a sequence of nonnegative real numbers satisfying s n+1 ≤ (1 − λ n ) s n + λ n δ n , ∀n ≥ 0, (15) where {λ n } and ...

Ishikawa iterative sequence with errors for strongly pseudocontractive operators in arbitrary Banach spaces

The Ishikawa iterative sequences with errors are studied for Lipschitzian strongly pseudo-contractive operators in arbitrary real Banach spaces; some well-known results of Chidume (1998) and Zeng (2001) are generalized.