Convergence Theorems for φ-Strongly Accretive and φ-Hemicontractive Operators

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

Convergence Theorems for the Zeros of a Finite Family of Generalized Φ-accretive Operators

A strong convergence theorem for the common zero for a finite family of Generalized Lipschitz operators in a uniformly smooth Banach space is proved when atleast one of the operator is Generalized Φaccretive, using a new iteration formula. Similar result for Generalized Lipschitz and Generalized Φpseudocontractive map is also proved. Our result extends the convergence results of Chidume [4] to ...

Strong Convergence Theorem for Fixed Points of Nearly Uniformly L−Lipschitzian Asymptotically Generalized Φ-Hemicontractive Mappings

Let C be a nonempty convex subset of a real Banach space E in which the normalized duality map is norm-to-norm uniformly continuous on bounded subsets of E. Let T be a nearly uniformly L−Lipschitzian asymptotically generalized Φ-hemicontractive map in the intermediate sense. An iterative process of the Manntype is proved to converge strongly to the unique fixed point of T . Under this setting, ...

On the Convergence of Multistep Iteration for Uniformly Continuous Φ-Hemicontractive Mappings

and Applied Analysis 3 In 2005, C. E. Chidume and C. O. Chidume 3 proved the convergence theorems for fixed points of uniformly continuous generalized Φ-hemicontractive mappings and published in 3 . However, there exists a gap in the proof course of their theorems. The aim of this paper is to show the convergence of the multistep iteration with errors for fixed points of uniformly continuous Φ-...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups