Browse > Article
http://dx.doi.org/10.4134/BKMS.2002.39.2.269

A NECESSARY AND SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE MANN SEQUENCE FOR A CLASS OF NONLINEAR OPERATORS  

Chidume, C.E. (The Avdus Salam International Centre for Theoretical Physics)
Nnoli, B.V.C. (Department of Mathematics, University of Jos)
Publication Information
Bulletin of the Korean Mathematical Society / v.39, no.2, 2002 , pp. 269-276 More about this Journal
Abstract
Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $\lambda\$\mid$x-Tx\$\mid$^2$, for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$. We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.
Keywords
demicontractive; condition(A); Banach spaces;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. P. Gossez and E. Lami Dozo, Some geometric properties related to the fixed point theory for nonexpansive mappings, Pacific. J. Math. 40 (1972), 565-573.   DOI
2 M. O. Osilike and A. Udomene, Demiclosedness principle and convergence theorems for stictly pseudocontractive mappings of the Browder-Petryshyn type, J. Math Anal. Appl. 256 (2001), no. 2, 431-445.   DOI   ScienceOn
3 W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.   DOI   ScienceOn
4 F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math Anal. Appl. 20 (1967), 297-228.   DOI
5 Z. Opial, Weak convergence of the sequence of successive approximation for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.   DOI
6 T. L. Hicks and J. R. Kubicek, On the Mann iteration process in Hilbert space, J. Math Anal. Appl. 59 (1977), 498-504.   DOI
7 Tan and Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math Anal. Appl. 178 (1993), 301-308.   DOI   ScienceOn
8 C. E. Chidume, The solution by iteration of nonlinear equations in certain Banach spaces, J. Nig. Math. Soc. 3 (1984), 57-62.
9 S. Maruster, The solution by iteration of nonlinear equations, Proc. Amer. Math. Soc. 66 (1977), 69-73.   DOI   ScienceOn
10 M. K. Ghosh and L. Debnath, Convergence of Ishikawa iterates of quasinonexpansive mappings, J. Math Anal. Appl. 207 (1997), 96-103.   DOI   ScienceOn