### Viscosity approximation method for split common null point problems between Banach spaces and Hilbert spaces

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Y. Censor, and T. Elfving: A multiprojection algorithm using Bregman projections in a product space. Numer. Algorithms, vol. 8, pp. 221-239, (1994).

SM. Alsulami and W. Takahashi: The split common null point problem for maximal monotone mappings in Hilbert spaces and applications. J. Nonlinear Convex Anal., vol.15, pp.793-808, (2014).

W. Takahashi, H-K. Xu and J-C. Yao: Iterative methods for generalized split feasibility problems in Hilbert spaces. Set-Valued Var. Anal. 23, pp. 205-221,(2015).

C. Byrne, Y. Censor, A. Gibali, and S. Reich: The split common null point problem. J. Nonlinear Convex Anal., vol. 13, pp. 759-775, (2012).

W. Takahashi: The split feasibility problem in Banach spaces. J. Nonlinear Convex Anal., vol. 15, pp. 1349-1355, (2014).

W. Takahashi: The split common null point problem in Banach spaces. Arch. Math. (Basel), vol. 104 (4), pp. 357-365, (2015).

W. Takahashi and J-C Yao:Strong convergence theorems by hybrid methods for the split common null point problem in Banach spaces, Fixed Point Theory and Applications, vol. 2015, article 87, (2015).

A. Moudafi: Viscosity approximation methods for fixed-point problems, J. Math. Anal. Appl., vol.241, pp. 46-55, (2000).

H.K. Xu: Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. vol. 298, pp. 279-291, (2004).

J.P. Gossez and E. Lami Dazo: Some geometric properties related to the fixed point theory for nonexpan- sive mappings, Pac. J. Math., vol. 40, pp. 565-573, (1972).

S-S. Chang, Y.J. ChoZhou, and H.Z. ZHou: Ilterative methods for nonlinear opertor equation in banach spaces, Nova Science Publishers Inc., Huntington, New York, (2002).

C. Chidume: Geometric Properties of Banach Spaces and Nonlinear Iterations,Lecture Notes in Mathe- matics, vol. 1965, Springer-Verlag London Limited, (2009).

R.T. Rockafellar: On the maximality of sums of nonliear monotone opertors,Trans. Amer. Math.Soc., vol. 149, pp. 77-85, (1970).

FE. Browder: Nonlinear maximal monotone operators in Banach spaces. Math. Ann. vol. 175, pp. 89-113, (1968).

K. Ayoma, F. Kohsaka and W.Takahashi: Strong convergence theorems for a family of mappings of type (P) and applications. Proceeding of the Asian Conference on Nonlinear Analysis and Optimization (Matsue, Japan, 2008), Japan, Yokohama Publishers Inc., pp.1-17, (2009).

S. Reich: Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., vol. 67, pp. 274-276, (1979).

S. Kitahara and W. Takahashi: Image recovery by convex combinations of sunny nonexpansive retractions,

Topological Methods in Nonlinear Anal., vol. 2, no. 2, pp. 333-342, (1993).

SS. Chang: Some problems and results in the study of nonlinear analysis. Nonlinear Anal., vol. 33, pp. 4197-4208, (1997).

H.K. Xu: Inequalities in Banach spaces with applications, Nonlinear Analysis, vol. 16 (12), pp. 1127-1138, (1991).

Cho, YJ, Zhou, HY, Guo, G: Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings. Comput. Math. Appl., vol. 47, pp. 707-717, (2004).

V. Barbu: Nonlinear Semigroups and Differential Equations in Banach Space. Noordhoff, Groningen, (1976).

R.T. Rockafellar: Characterization of subdifferencetials of convex function. Pacific J.Math., vol. 17, pp. 497-510, (1966).

R.T. Rockafellar: On maximal monotonicity of subdifferencetial mappings. Pacific J.Math., vol. 33, pp. 209-216, (1970).

F. E. Browder: Fixed-point theorems for noncompact mappings in Hilbert space, Proceedings of the National Academy of Sciences of the United States of America, vol. 53, pp. 1272-1276, (1965).

T. Suzuki: Strong convergence of Krasnoselskii and Mann’s type sequence for one-parameter nonexpansive semigroup without Bochner integrals, J. Math. Anal. Appl., vol. 305, pp. 227-239, (2005).

H.K. Xu: Iterative algorithms for nonlinear operators. J. Lond. Math. Soc. , vol. 66, pp. 240-256, (2002).

W. Takahashi: Introduction to Nonlinear and Convex Analysis, Yokohama Publishers, Yokohama, (2009).

DOI: http://dx.doi.org/10.26713%2Fjims.v9i1.380

eISSN 0975-5748; pISSN 0974-875X