ISHIKAWA ITERATIVE SEQUENCE WITH ERRORS FOR φ-STRONGLY ACCRETIVE 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.

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.

The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of theMann iterationmethod and the Ishikawa iterationmethod for φ-pseudocontractive operators in nonempty closed convex subsets of unifor...

Convergence of Ishikawa iterative sequence for strongly pseudocontractive operators in arbitrary Banach spaces

Under the condition of removing the restriction any bounded, we give the convergence of the Ishikawa iteration process to a unique fixed point of a strongly pseudocontractive operator in arbitrary real Banach space. Furthermore, general convergence rate estimate is given in our results, which extend the recent results of Ciric [3] and Soltuz [12]. AMS subject classifications: Primary 47H10; Sec...

A three-step iterative scheme for solving nonlinear φ-strongly accretive operator equations in Banach spaces