On convergence of random iterative schemes with errors for strongly pseudo-contractive Lipschitzian maps in real Banach spaces

Volume 9, Issue 5, pp 3157--3168 http://dx.doi.org/10.22436/jnsa.009.05.105

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Satish Narwal - Department of Mathematics, S. J. K. College Kalanaur, Rohtak 124113, India. Renu Chugh - Department of Mathematics, M. D. University, Rohtak 124001, India. Vivek Kumar - Department of Mathematics, K. L. P. College, Rewari 123401, India.

Abstract

In this work, strong convergence and stability results of a three step random iterative scheme with errors for strongly pseudo-contractive Lipschitzian maps are established in real Banach spaces. Analytic proofs are supported by providing numerical examples. Applications of random iterative schemes with errors to find solution of nonlinear random equation are also given. Our results improve and establish random generalization of results obtained by Xu and Xie [Y. Xu, F. Xie, Rostock. Math. Kolloq., 58 (2004), 93-100], Gu and Lu [F. Gu, J. Lu, Math. Commun., 9 (2004), 149-159], Liu et al. [Z. Liu, L. Zhang, S. M. Kang, Int. J. Math. Math. Sci., 31 (2002), 611-617] and many others.

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Keywords

• Random Iterative schemes
• stability
• strongly pseudo-contractive maps.

MSC

•  47H10
•  47H06

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