Abstract

In this paper, we prove strong convergence results for some Jungck type iterative schemes in Convex metric spaces for a pair of non-selfmappings using a certain contractive condition. Our results generalize existing results in the literature.

References

• Singh, S. L. , Bhatnagar, C. and Mishra S. N. 2005. Stability of Jungck type iterative procedures. International Journal of Mathematics and Mathematical Sciences. 19 (2005), 3035–3043.
• Olatinwo, M. O. Some stability and strong convergence results for the Jungck-Ishikawa iteration process. Creative Mathematics and Informatics. 17 (2008), 33–42.
• Bosede, A. O. 2010. Strong convergence results for the Jungck-Ishikawa and Jungck-Mann iteration processes. Bulletin of Mathematical Analysis and Applications. 2 (2010), 65–73.
• Olaleru, J. O. and Akewe, H. 2010. On multistep iterative scheme for approximating the common fixed points of contractive-like operators. International Journal of Mathematics and mathematical Sciences. 2010 (2010), Article ID 530964, 1-11.
• Olatinwo, M. O. 2008. A generalization of some convergence results using a Jungck-Noor three-step iteration process in arbitrary Banach space, Polytechnica Posnaniensis. 40 (2008), 37–43.
• Chugh, R. and Kumar, V. 2011. Strong Convergence and Stability results for Jungck-SP iterative scheme. International Journal of Computer Applications. 36 (2011), 21-27.
• Phuengrattana, W. and Suantai, S. 2011. On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval. Journal of Computational and Applied Mathematics. 235 (2011), 3006–3014.
• Noor, M. A. 2000. New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications. 251 (2000), 217–229.
• Ishikawa, S. 1974. Fixed points by a new iteration method," Proceedings of the American Mathematical Society. 44 (1974), 147–150.
• Mann, W. R. 1953. Mean value methods in iteration. Proceedings of the American Mathematical Society. 4 (1953), 506–510.
• Agarwal, R. P. , O'Regan, D. and Sahu, D. R. 2007. Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. Journal of Nonlinear and Convex Analysis. 8 (2007), 61–79.
• Sahu, D. R. and Petrus¸el, A. 2011. Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces. Nonlinear Analysis: Theory, Methods & Applications. 74 (2011) 6012–6023.
• Hussain, N. , Jungck, G. and Khamsi, M. A. 2012. Nonexpansive retracts and weak compatible pairs in metric spaces. Fixed Point Theory and Applications. 2012 (2012) article 100, 1-10.
• Jungck, G. and Hussain, N. 2007. Compatible maps and invariant approximations. Journal of Mathematical Analysis and Applications. 325 (2007) 1003–1012.
• Takahashi, W. 1970. A convexity in metric spaces and nonexpansive mapping. Kodai Math. Sem. Rep. 22 (1970), 142-149.
• Hussain, N. , Kumar, V. and Kutbi, M. A. 2013. On rate of Convergence of Jungck type iterative schemes. Abstract and Applied Analysis. 2013 (2013), Article ID 132626, 15 pages.