STABILITY OF ITERATIVE PROCESSES WITH ERRORS FOR NONLINEAR EQUATIONS OF φ-STRONGLY ACCRETIVE TYPE OPERATORS

Abstract

In this paper, we study the stability of the Mann and Ishikawa iterative processes with errors for the nonlinear equations of φ-strongly accretive type operators in arbitrary real Banach spaces. We also study the stability of the Mann and Ishikawa iterative processes with errors for the iterative approximation of fixed point of Lipschitzian and φ-hemicontractive operators in arbitrary real Banach spaces.

^†The second author was supported by '98 APEC Post-Doctor Fellowship (KOSEF) while he visited Gyeongsang National University and the third author wishes to acknowledge the financial support of the Korea Research Foundation Grant (KRF-99-005-D00003).

Keywords:

• Stability
• Mann and Ishikawa iterative processes with errors
• Nonlinear φ-strongly pseudocontractive operators
• φ-Strongly accretive operators
• φ-Hemicontractive operators
• 1991 Mathematics Subject Classification: 47H06; 47H15; 47H17

Acknowledgments

Notes

^†The second author was supported by '98 APEC Post-Doctor Fellowship (KOSEF) while he visited Gyeongsang National University and the third author wishes to acknowledge the financial support of the Korea Research Foundation Grant (KRF-99-005-D00003).