The purpose of this paper is to introduce more general modified two step and three step Ishikawa iterative with errors for local strongly pseudo contractive and local strongly accretive mappings which is much more general than the important class of strongly pseudo contractive and strongly accretive mappings. Also, we study the convergence of this iteration for locally mappings in the framework of Banach space. The results presented in this paper improve, generalize of the results of Mogbademn and OlaleauRafq, Yuguang and Fang and others.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 6)

Pages:

13-23

Citation:

S. Salman Ab and Z. H. Mabee, "Modified Three-Step Iteration Process with Errors for Three Local Strongly Pseudo Contractive Operators", The Bulletin of Society for Mathematical Services and Standards, Vol. 6, pp. 13-23, 2013

Online since:

Jun 2013

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

Liu Z. , Kang S.M. and Shim S.H. Almost stability of the Mann iteration method with errors for strictly Hemi-contractive operators in smooth Banach spaces, Korean Math S.C. 40(2003) pp. (22-40).

Gurudwan. N. and Sharma. B.K. convergence theorems for the zeros of a finite family of Generalized - accretive operators, J. Non linear sci Appl. 2(2009) pp. (260-269).

Mogbademu A.A. and Olalean J.O. modified Noor iterative methods for a family of strongly pseudo contractive maps, Bull of Math. Appl. 2(2011). Pp0(132-139).

Noor M.A. , Rassia T.M. and Huang .Z. three step iteration for Non linear accretive operators equations, J. Math . Aual. Appl. 274(2002) pp. (59-68).

Owojori O. O. and Imoru c. o A general Ishikawa iteration sequence for non linear uniformly continuous pseudo- contractive operators in Arbitrary Banach spaces, proc. Jung. Math. Soc, 4(2002) pp. (91-100).

Owojori O. O. and Imoru c. o New iteration methods for pseudo- contractive and accretive operators in Arbitrary Banach spaces, krag.J. Math, 25(2003) pp. (97-110).

Rafiq .A. Modified Noor iterations for non linear equations in Banach spaces, Appl. Math. Comput. 182(2006) pp. (589-595).

Rafiq .A. Mann. Accretive scheme for non linear equations, Math. Comun. 12(2007) pp. (25-31).

Xue Z. and Fan. R. some comments on Noor's iterations is Banach spaces, Appl. Math. Comput. 206(2008) pp. (12-15).

Yany L. the equivalence of Ishikawa Mann and Multi-self iterations is Banach spaces, A Joural of Chinese univ., 16(2007) pp. (83-91).

Yugang. Xu, Fang XIE. Stability of Mann iterations process with Random errors for the fixed point of strongly pseudo contractive mapping in Arbitrary Banach spaces, math. Kolloq 58(2004) pp. (93-100).

Zeqing, L., Yuguang, X and shim. K.M. almost stable iterations schemes for local strongly pseudo contractive and local strongly accretive operators in real uniformly smooth Banach spaces, Aeta. Math , 2(2008). Pp. (285-298).