Convergence Theorems of Common Fixed Points for Pseudocontractive Mappings

Convergence Theorems of Common Fixed Points for Pseudocontractive Mappings

where E∗ denotes the dual space of E and 〈·, ·〉 denotes the generalized duality pairing. In the sequel, we denote a single-valued normalized duality mapping by j. Throughout this paper, we use F T to denote the set of fixed points of the mapping T . ⇀ and → denote weak and strong convergence, respectively. Let K be a nonempty subset of E. For a given sequence {xn} ⊂ K, let ωω xn denote the weak...

Convergence Theorems for Fixed Points of Demicontinuous Pseudocontractive Mappings

Let D be an open subset of a real uniformly smooth Banach space E. Suppose T : D̄ → E is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where D̄ denotes the closure ofD. Then, it is proved that (i) D̄ ⊆ (I + r(I −T)) for every r > 0; (ii) for a given y0 ∈ D, there exists a unique path t → yt ∈ D̄, t ∈ [0,1], satisfying yt := tT yt + (1− t)y0. Moreover, if F(T) = ∅ o...

The Convergence Theorems for Common Fixed Points of Uniformly L-lipschitzian Asymptotically Φ-pseudocontractive Mappings

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...

Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Pseudocontractive Mappings

Strong Convergence Theorems of Common Fixed Points for a Family of Quasi--Nonexpansive Mappings