Jungck-Khan iterative scheme and higher convergence rate

References

• R.P. Agarwal, D. O'Regan, and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8 (2007), pp. 61–79.
   Web of Science ®Google Scholar
• A. Alotaibi, V. Kumar, and N. Hussain, Convergence comparison and stability of Jungck-Kirk-type algorithms for common fixed point problems, Fixed Point Theory Appl. 2013 (2013), pp. 1–30. doi: 10.1186/1687-1812-2013-173
   Web of Science ®Google Scholar
• V. Berinde, Picard iteration converges faster than the Mann iteration in the class of quasi-contractive operators, Fixed Point Theory Appl. 2 (2004), pp. 97–105. doi: 10.1155/S1687182004311058
   Google Scholar
• V. Berinde, Iterative Approximation of Fixed Points, Springer Berlin Heidelberg, Berlin, 2007.
   Google Scholar
• R. Chugh and V. Kumar, Data dependence of Noor and SP iterative schemes when dealing with quasi-contractive operators, Int. J. Comput. Appl. 40 (2011), pp. 41–46.
   Google Scholar
• L.B. Ciric, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd) (NS). 12(26) (1971), pp. 19–26.
   Google Scholar
• L.B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45(2) (1974), pp. 267–273. doi: 10.2307/2040075
   Web of Science ®Google Scholar
• M. De la Sen and E. Karapinar, On a cyclic Jungck modified TS-iterative procedure with application examples, Appl. Math. Comput. 233 (2014), pp. 383–397. doi: 10.1016/j.amc.2014.02.008
   Web of Science ®Google Scholar
• F. Gürsoy, Applications of normal S-iterative method to a nonlinear integral equation, The Scientific World Journal 2014 (2014), pp. 1–5. doi: 10.1155/2014/943127
   Web of Science ®Google Scholar
• F. Gürsoy, V. Karakaya, and B. Rhoades, Data dependence results of new multi-step and S-iterative schemes for contractive-like operators, Fixed Point Theory Appl. 76 (2013), pp. 1–12.
   Google Scholar
• N. Hussain, V. Kumar, and M.A. Kutbi, On the rate of convergence of Jungck-type iterative schemes, Abstr. Appl. Anal. 2013 (2013), pp. 1–15. Article ID 132626.
   Google Scholar
• G. Jungck, Commuting mappings and fixed points, Amer. Math. Mon. 83(4) (1976), pp. 261–263. doi: 10.2307/2318216
   Web of Science ®Google Scholar
• G. Jungck and N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2007), pp. 1003–1012. doi: 10.1016/j.jmaa.2006.02.058
   Web of Science ®Google Scholar
• V. Karakaya, K. Doğan, F. Gürsoy, and M. Ertürk, Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstr. Appl. Anal. 2013 (2013), pp. 1–9. Article ID 560258.
   Google Scholar
• A.R. Khan, On modified Noor iterations for asymptotically nonexpansive mappings, Bull. Belg. Math. Soc. Simon Stevin. 17 (2010), pp. 127–140.
   Web of Science ®Google Scholar
• A.R. Khan, V. Kumar, and N. Hussain, Analytical and numerical treatment of Jungck-type iterative schemes, Appl. Math. Comput. 231 (2014), pp. 521–535. doi: 10.1016/j.amc.2013.12.150
   Web of Science ®Google Scholar
• V. Kumar, A. Latif, A. Rafiq, and N. Hussain, S-iteration process for quasi-contractive mappings, J. Inequal. Appl. 2013 (2013), pp. 1–15. doi: 10.1186/1029-242X-2013-1
   Web of Science ®Google Scholar
• M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251(1) (2000), pp. 217–229. doi: 10.1006/jmaa.2000.7042
   Web of Science ®Google Scholar
• M.O. Olatinwo, A generalization of some convergence results using the Jungck-Noor three-step iteration process in arbitrary Banach space, Fasc. Math. 40 (2008), pp. 37–43.
   Google Scholar
• M.O. Olatinwo, Some stability and strong convergence results for the Jungck-Ishikawa iteration process, Creative Math Inf. 17 (2008), pp. 33–42.
   Google Scholar
• O. Popescu, Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Math. Commun. 12 (2007), pp. 195–202.
   Google Scholar
• S.L. Singh, C. Bhatnagar, and S.N. Mishra, Stability of Jungck-type iterative procedures, Int. J. Math. Math. Sci. 19 (2005), pp. 3035–3043. doi: 10.1155/IJMMS.2005.3035
   Google Scholar
• S.M. Soltuz and T. Grosan, Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl. 2008 (2008), pp. 1–7. Article ID 242916. doi: 10.1155/2008/242916
   Web of Science ®Google Scholar
• W. Takahashi and S. Matsushita, Strong convergence theorems for nonexpansive nonself-mappings without boundary conditions, Nonlinear Anal. 68 (2008), pp. 412–419. doi: 10.1016/j.na.2006.11.007
   Web of Science ®Google Scholar
• X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 113 (1991), pp. 727–731. doi: 10.1090/S0002-9939-1991-1086345-8
   Web of Science ®Google Scholar