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Strong convergence of Picard and Mann iterations for strongly demicontractive multi-valued mappings.
- Source :
-
Carpathian Journal of Mathematics . 2020, Vol. 36 Issue 2, p269-276. 8p. - Publication Year :
- 2020
-
Abstract
- A class of demicontractive mappings was first introduced in [Hicks, T. L. and Kubicek, J. D., On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl., 59 (1977) 498-504 and Maruster, S., The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc., 63 (1977), 69-73] and was first mentioned in the case of multi-valued mappings in [Chidume, C. E., Bello, A. U. and Ndambomve, P., Strong and δ-convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT(0) spaces, Abstr. Appl. Anal., 2014 (2014), https://doi.org/10.1155/2014/805168 and Isiogugu, F. O. and Osilike, M. O., Convergence theorems for new classes of multivalued hemicontractive-type mappings, Fixed Point Theory Appl., 2014 (2014), https://doi.org/10.1186/1687-1812-2014-93]. The demicontractivity with some weak smoothness conditions ensures only weak convergence of Mann iteration. In 2015, Marus,ter and Rus [Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 2, 173-182], introduced a class of strongly demicontractive mappings, and also discussed some relationships between strongly demicontractive mappings and Kannan contractions. In this paper, we introduce a new class of strongly demicontractive multivalued mappings in Hilbert spaces. Strong convergence theorems of Picard and Mann iterative methods for strongly demicontractive multi-valued mappings are established under some suitable coefficients and control sequences. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15842851
- Volume :
- 36
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Carpathian Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 144293845
- Full Text :
- https://doi.org/10.37193/cjm.2020.02.10