**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32009

##### Algorithms for Computing of Optimization Problems with a Common Minimum-Norm Fixed Point with Applications

**Authors:**
Apirak Sombat,
Teerapol Saleewong,
Poom Kumam,
Parin Chaipunya,
Wiyada Kumam,
Anantachai Padcharoen,
Yeol Je Cho,
Thana Sutthibutpong

**Abstract:**

**Keywords:**
σ-asymptotically quasi-nonexpansive nonselfmapping,
strong convergence,
fixed point,
uniformly convex and
uniformly smooth Banach space.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1339698

**References:**

[1] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mapping, Proc. Amer. Math. Soc. 35(1972), 171-174.

[2] C. E. Chidume, E. U. Ofoedu, H. Zegeye, Strong and weak convergence theorems for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 280(2003), 364–374.

[3] L. Wang, Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J. Math. Anal. Appl. 323(2006), 550-557.

[4] W. Guo, W. Guo, Weak convergence theorems for asymptotically nonexpansive nonself-mappings, Appl. Math. Lett. 24(2011), 2181-2185.

[5] W. Guo, Y. J. Cho, W. Guo, Convergence theorems for mixed type asymptotically nonexpansive mappings, Fixed Point Theory and Applications. 2012 2012:224.

[6] H. Zegeye, N. Shahzed, Approximation of the common minimum-norm fixed point of a finite family of asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2013 2013:1, 12 pages.

[7] J. Schu, Iteration construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158(1991), 407-413.

[8] M. O. Osilike, S. C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling. 256(2001), 431-445.

[9] Y.I. Alber, Metric and generalized projection opeators in Banach spaces: properties and applications, in: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Lecture Notes in Pure and Applied Mathematics, Dekker, New York, 1996, pp. 1550.

[10] C. Byrne, Iterative oblique projection onto convex subset and the split feasibility problem, Inverse Problems. 18 (2002), 441-453.

[11] H. K. Pathak, V. K. Sahu, Y. J. Cho, Approximation of a common minimum-norm fixed point of a finite family of σ-asymptotically quasi-nonexpansive mappings with applications, J. Nonlinear Sci. Appl. 9 (2016), 3240-3254.

[12] Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problem in intensity-modulated radiation therapy, Phys. Med. Biol. 51(2006), 2353-2365.

[13] Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projection in a product space, Numer. Algoritms. 8 (1994), 221-239.

[14] X. Yang, Y. C. Liou, Y. You, Finding minimum-norm fixed point of nonexpansive mapping and applications, Math. Problem in Engin. Article ID 106450, (2011), 13 pp.

[15] Y. Hao, S. Y. Cho, X. Qin, Some weak convergence theorems for a family of asymptotically nonexpansive nonself mappings, Fixed Point Theo. Appl. 2010, Article ID 218573, 11 pp.

[16] S. Kamimura, W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim. 13 (2002) 938-945.

[17] J. G. Ohara, P. Pillay, H. K. Xu, Iteration approaches to convex feasibility problem in Banach spaces, Nonlinear Anal. 64 (2006), 2022-2042.

[18] P. E. Manige, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minization, Set-Valued Anal, 16 (2008), 899-912.

[19] H. Zegeye, E. U. Ofoedu, N. Shahzad, Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings, Appl. Math. Comput. 216 (2010), 3439-3449