Search    
Login
Individual Subscriber Registration
Login Forgot Password?
 
Author Login
Author Registration
Login Forgot Password?
Journal Menu

  JP Journal of Fixed Point Theory and Applications  
 ISSN: 0973-4228
 
 
 

     JP Journal of Fixed Point Theory and Applications
    Volume 2, Issue 3, Pages 231 - 246 (December 2007)


THE EQUIVALENCE BETWEEN THE CONVERGENCES OF PERTURBED MANN AND ISHIKAWA ITERATIONS FOR f-STRONGLY PSEUDOCONTRACTIVE MAPS AND f-STRONGLY ACCRETIVE OPERATORS

D. I. Igbokwe (Nigeria)

Received October 18, 2007

References:



[1] F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl. 20 (1967), 197-228.

[2] C. E. Chidume and C. Moore, Fixed point iteration for pseudocontractive maps, Proc. Amer. Math. Soc. 127(4) (1999), 1163-1170.

[3] C. E. Chidume and S. A. Mutangadura, An example on the Mann iteration method for Liptschitz pseudocontractions, Proc. Amer. Math. Soc. 129(8) (2001), 2359-2363.

[4] C. E. Chidume and M. O. Osilike, Nonlinear accretive and pseudocontractive operator equations in Banach spaces, Nonlinear Anal. 31(7) (1998), 779-789.

[5] T. L. Hicks and J. D. Kubicek, On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl. 59 (1977), 498-504.

[6] D. I. Igbokwe, Construction of fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type in arbitrary Banach spaces, Fixed Point Theory Appl., Vol. 4, Y. J. Cho et al., eds., Nova Science Publishers, Inc., New York, 2003, pp. 137-147.

[7] I. S. Ishikawa, Fixed points by new iteration method, Proc. Amer. Math. Soc. 149 (1974), 147-150.

[8] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520.

[9] L. S. Liu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125.

[10] Z. Liu, J. K. Kim and S. M. Kang, Necessary and sufficient conditions for convergence of Ishikawa iterative schemes with errors to f-Hemicontractive mappings, Commun. Korean Math. Soc. 18(2) (2003), 251-261.

[11] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.

[12] C. Moore and B. V. C. Nnoli, Local iterations for fixed points of uniformly hemicontractive maps in arbitrary normed linear spaces, Soochow J. Math 27(1) (2001), 59-72.

[13] M. O. Osilike, Iteration solution of nonlinear equations of the f-strongly accretive type, J. Math. Anal. Appl. 200(20) (1996), 259-271.

[14] M. O. Osilike, Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type, J. Math. Anal. Appl. 213(1) (1997), 91-105.

[15] M. O. Osilike and D. I. Igbokwe, Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations, Comput. Math. Appl. 40 (2000), 559-567.

[16] L. Qihou, On Niampally and Singh’s open questions, J. Math. Anal. Appl. 124 (1987), 157-164.

[17] L. Qhiou, The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings, J. Math. Anal. Appl. 148 (1990), 55-62.

[18] B. E. Rhoades, Comments on two fixed point iteration methods, J. Math. Anal. Appl. 183 (1994), 118-120.

[19] B. E. Rhoades and S. M. Soltuz, On the equivalence of Mann and Ishikawa iteration methods, Internat. J. Math. Sci. 33 (2003), 451-459.

[20] B. E. Rhoades and S. M. Soltuz, The equivalence between the convergence of Ishikawa and Mann iterations for an asymptotically pseudocontractive map, J. Math. Anal. Appl. 283 (2003), 681-688.

[21] K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.

[22] Y. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101.

Keywords and phrases: f-strongly pseudocontractive maps, f-strongly accretive operators, perturbed Mann iteration method, perturbed Ishikawa iteration method, fixed points.

 


Previous Article   

 
         

© Copy Right  PUSHPA PUBLISHING HOUSE, Vijaya Niwas, 198, Mumfordganj, Allahabad-211002, India