Convergence Theorems of Iterative Schemes For Nonexpansive Mappings
DOI:
https://doi.org/10.24297/jam.v12i12.1074Abstract
In this paper, we give a type of iterative scheme for sequence of nonexpansive mappings and we study the strongly convergence of these schemes in real Hilbert space to common fixed point which is also a solution of a variational inequality. Also there are some consequent of this results in convex analysisDownloads
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References
[1] H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer-Verlag, 2011.
[2] J.M. Borwein and J.D. Vanderwerff, Convex Functions, Cambridge University Press, 2010.
[3] R.S. Burachik and A.N. Iusem, Set-Valued Mappings and Enlargements of monotone Operators, Springer-Verlag, 2008.
[4] S. Simons, From Hahn-Banach to Monotonicity, Springer-Verlag, 2008.
[5] C. Z ˘alinescu , Convex Analysis in General Vector Spaces,world Scientific Publishing, 2002.
[6].A .Moudafi, Viscosity approximation method for fixed point problem, Appl. 241 (2000) 46-55.
[7]. H. H .Bauschke,S.M.Moffat and X.Wang,"Firmly nonexpansvie mappings and maximally monotone operators correspondence and duality"set valued variational analysis ,vol 20,(2012),131_153.
[8] .K .Geobel and A. Kirk ,"Topics in metric fixed point theory in Cambridge studies in advanced mathematics,"vol,28,Cambridge univ.press(1990).
[9].H.K .Xu ,"Iterative Algorithm for nonlinear operators",J .london Math .soc .66(2002) 240-256.
[10].D.A . Ruiz ,G .L .Acedo and V. M. Marquez ,"Firmly nonexpansive mappings",J nonlinear analysis,vol 15(2014)1
[11].R.T.Rockafellar,"On the maximal monotonicity of subdifferential mappingss",pacific J.Math.33(1970),209-216.
[2] J.M. Borwein and J.D. Vanderwerff, Convex Functions, Cambridge University Press, 2010.
[3] R.S. Burachik and A.N. Iusem, Set-Valued Mappings and Enlargements of monotone Operators, Springer-Verlag, 2008.
[4] S. Simons, From Hahn-Banach to Monotonicity, Springer-Verlag, 2008.
[5] C. Z ˘alinescu , Convex Analysis in General Vector Spaces,world Scientific Publishing, 2002.
[6].A .Moudafi, Viscosity approximation method for fixed point problem, Appl. 241 (2000) 46-55.
[7]. H. H .Bauschke,S.M.Moffat and X.Wang,"Firmly nonexpansvie mappings and maximally monotone operators correspondence and duality"set valued variational analysis ,vol 20,(2012),131_153.
[8] .K .Geobel and A. Kirk ,"Topics in metric fixed point theory in Cambridge studies in advanced mathematics,"vol,28,Cambridge univ.press(1990).
[9].H.K .Xu ,"Iterative Algorithm for nonlinear operators",J .london Math .soc .66(2002) 240-256.
[10].D.A . Ruiz ,G .L .Acedo and V. M. Marquez ,"Firmly nonexpansive mappings",J nonlinear analysis,vol 15(2014)1
[11].R.T.Rockafellar,"On the maximal monotonicity of subdifferential mappingss",pacific J.Math.33(1970),209-216.
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Published
2017-01-28
How to Cite
Ali Hadi, I. M., & Salman Abd, D. salwa. (2017). Convergence Theorems of Iterative Schemes For Nonexpansive Mappings. JOURNAL OF ADVANCES IN MATHEMATICS, 12(12), 6845–6851. https://doi.org/10.24297/jam.v12i12.1074
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