Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spaces

✍ Scribed by Ljubomir B. Ćirić; Jeong Sheok Ume

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 151 KB
• Volume: 278
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310298

✦ Synopsis

Abstract

The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D ⊂ X → 2^D^ be a multi‐valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)