Picard-Mann Hybrid Iteration Processes for Monotone Non Expansive Mappings

B.Geethalakshmi.; R.Hemavathy

doi:https://doi.org/10.14445/22315373/IJMTT-V55P548

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 55 | Number 5 | Year 2018 | Article Id. IJMTT-V55P548 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P548

Picard-Mann Hybrid Iteration Processes for Monotone Non Expansive Mappings

B.Geethalakshmi.,R.Hemavathy

Abstract

In this paper we prove strong convergence and stability results of Picard-Mann hybrid iteration scheme for a monotone non expansive mappings in a Uniformly Convex Banach space.

Keywords

Strong convergence, Picard –Mann hybrid iteration scheme, monotone nonexpansive mapping.

References

1. A. M. Soleimani, H.Vaezpour SM, Rhoades B.E. (2009), On T-stability of Picard’s Iteration in cone metric space, Fixed point theory appl.DOl: 10.1155/2009/751090.
2.Berinde, V.Iterative Approximation of fixed points EditurraEfemeride, Baia Mare (2002).
3.B.Dehaish and Khamsi, Mann iteration process for monotone nonexpansive mappings, Fixed point theory and applications (2015) 2015:177 DOI 10.1186/s 13663-015-0416-0
4. Browder, FE: Nonexpansive nonlinear operators in a Banach Space. Proc. Natl. Acad. Sci. USA 54,1041-1044(1965).
5.Bachar, M.khamsi, MA: On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces. Fixed Point Theory Appl.2015,160 (2015)
6. J.G.Flaset, E.L. Fluster and T. Suzuki, Fixed point theory for a class of generalised non-expansive mapping. J.Math.Anal.Appl.375(1) (2011), 185-195.
7. Gohde, D: ZumPrinzip der kontraktivenabbildung. Math. Nachr.30,251-258.
8. Harder, AM: Fixed pointtheory and stability results for fixed point iteration procedures. Ph.d. thesis, University of Missouri-Polla(1987).
9. Hussai.N, Chugh, R.Kumar, V.Rafiq, On the rate of convergence of Kirk-type iterative schemes. J. Appl.Math. 345(2) (2012), 186-190,
10. Khan, SH: A Picard-Mann hybrid iterative process, Fixed point theory Appl 2013 Article ID69(2013). Dol 10.1186/11687-1812-2013- 69.
11.Lael.F and Heidarpour.Z, Fixed point theorems for a class of generalised nonexpansive mappings, Fixed point theory Appl, 2016:82. DOI .10,1186/S13663-016-0571-4.
12. Phuengrattana, W.Suantal, On the convergence of Mann, Ishikawa, Noor and Sp-iterations for continuous functions on an arbitrary integral. J.Comput. Appl. Math.235(9), 3006-3014 (2011).
13. Rhoades B.E. (1990), Fixed point theorems and stability results for fixed point iteration procedures, Indian J.PureAppl.Math 21:1-9.
14.Rhoades B.E, Soltuz SM (2006) ,The equivalence between the T-Stabilities of Mann and Ishikawa Iteration. J Math Anal Appl 318: 472- 475.
15. Xu, HK: Inequality in Banach Spaces with Applications,Nonlinear Anal.16, 1127-1138 (1991).
16.Y.Song, PoomKumam and Y.J Cho, Fixed point theorems and iterative approximations for monotone nonexpansive mappings in orderedBanachspace, Fixed point theory and applications (2016) 2016:73DOl 10.1186/s 13663-016-0563-4

Citation :

B.Geethalakshmi.,R.Hemavathy, "Picard-Mann Hybrid Iteration Processes for Monotone Non Expansive Mappings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 5, pp. 367-370, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P548