Abstract
In this paper, we are concerned with the study of an iterative scheme with errors involving two hemicontractive mappings. We approximate the common fixed points of these two mappings by weak and strong convergence of the iteration process in Hilbert space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Browder F.E., Petryshyn W.V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 20, 197–228 (1967)
Byrne C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 20, 103–120 (2004)
Chidume C.E., Moore C.: Fixed point iteration for pseudocontractive maps. Proc. Am. Math. Soc. 127(4), 1163–1170 (1999)
Giannessi, F., Maugeri, A., Pardalos, P.M. (eds): Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Nonconvex Optimization and Its Applications. Kluwer, New York (2003)
Genel A., Lindenstrass J.: An example concerning fixed points. Isr. J. Math. 22, 81–86 (1975)
Miao Y.: A modification of Mann’s iteration scheme. East J. Approx. 13(2), 211–221 (2007)
Opial Z.: Weak convergence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73, 591–597 (1967)
Osilike M.O., Aniagbosor S.C., Akuchu B.G.: Fixed points of asymptotically demicontractive mappings in arbitrary Banach. PanAm. Math. J. 12, 77–88 (2002)
Osilike M.O., Udomene A.: Demiclosedness principle and convergence results for strictly pseudocontractive mappings of Browder-Petryshyn type. J. Math. Anal. Appl. 256, 431–445 (2001)
Pardalos, P.M., Rassias, T.M., Khan, A.A. (eds): Nonlinear Analysis and Variational Problems. In Honor of George Isac. Springer Optimization and Its Applications 35. Springer, New York (2010)
Podilchuk C.I., Mammone R.J.: Image recovery by convex projections using a least-squares constraint. J. Opt. Soc. Am. A 7, 517–521 (1990)
Rafiq A.: On Mann iteration in Hilbert spaces. Nonlinear Anal. 66(10), 2230–2236 (2006)
Schu J.: Weak and strong convergence to fixed points of asympotically nonexpansive mappings. Bull. Austral. Math. Sco. 43, 153–159 (1991)
Reich S.: Weak convergence theorems for nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 67, 274–276 (1979)
Song Y.S.: On a Mann type implicit iteration process for continuous pseudo-contractive mappings. Nonlinear Anal. 67(11), 3058–3063 (2006)
Sezan M.I., Stark H.: Applications of convex projection theory to image recovery in tomography and related areas. In: Stark, H. (eds) Image Recovery Theory and Applications, pp. 415–462. Academic Press, Orlando (1987)
Sun Z.H.: Strong convergence of an implicit iteration process for a finite family of asymptotically quasinonexpansive mappings. J. Math. Anal. Appl. 286, 351–358 (2003)
Xu H.K., Kim T.H.: Strong convergence of modified Mann iterations. Nonlinear Anal. 61, 51–60 (2005)
Youla D.: Mathematical theory of image restoration by the method of convex projections. In: Stark, H. (eds) Image Recovery Theory and Applications, pp. 29–77. Academic Press, Orlando (1987)
Youla D.: On deterministic convergence of iterations of relaxed projection operators. J. Vis. Commun. Image Represent. 1, 12–20 (1990)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Miao, Y., Shen, L. Convergence of iterates with errors of semicontractive mappings. J Glob Optim 50, 221–227 (2011). https://doi.org/10.1007/s10898-010-9562-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-010-9562-4