Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces
In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition
C. Byrne, ``"Iterative oblique projection onto convex subsets and the split feasibility problems", Inverse Probl. 18 (2002) 441.
Y. Censor & A. Segal, "``The split common fixed point problem for directed operators", J. Convex Anal. 16 (2009) 587.
B.C. Deng, T. Chen & Y. L. Yin, ``"Strong convergence theorems for mixed equilibrium problem and asymptotically I-nonexpansive mapping in Banach spaces", Abstract and Applied Anal. 2014 (2014) 965737.
L. Yang, S. S. Chang, Y. J. Cho & J.K. Kim," ``Multiple-set split feasibility problems for total asymptotically strict pseudocontractions mappings", Fixed Point Theory Appl. 1 (2011) 77.
B. Qu & N. Xiu, "``Note on the CQ algorithm for the split feasibility problem", Inverse Probl. 21 (2005) 1655.
F. Schopfer, ``"Iterative Methods for the Solution of the Split Feasibility Problem in Banach Spaces", der Naturwissenschaftlich-Technischen Fakultaten, Universitat des Saarlandes, 2007.
A. Moudafi, `"`The split common fixed point problem for demi-contractive mappings", Inverse Probl. 26 (2014).
S. S. Chang, Y. J. Cho, J. K. Kim, W. Zhang & L. Yang, "Multiple-set split feasibility problems for asymptotically strict pseudocontractions", Abstr. Appl. Anal. 2012 (2012) 491760.
X. F. Zhang, L. Wang, Z. L. Ma & L. J. Qin `,`"The strong convergence theorems for split common fixed point problem of asymptotically nonexpansive mappings in Hilbert spaces", Journal of Inequalities and Applications 1 (2015) 1.
W. Takahashi, ``"The split common null point problem in Banach spaces", Arch. Math. (Basel) 104 (2015) 357.
J. Tang, S. S. Chang, L. Wang & X. Wang, ``"On the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings in Banach spaces", Journal of Inequalities and Applications 2015 (2015) 305.
J. A. Clarkson, "``Uniformly convex spaces", Trans. Am. Math. Soc. 40 (1936) 396.
C. E. Chidume, "Geometric properties in Banach spaces and nonlinear iterations"}, Springer-Verlag London Limited, 2009.
F. Shopfer, T. Schuster and A. K. Louis, "``Metri and Bregman projection onto affine subspaces and theircomputation via sequential subspace optimization methods", J. Inv. III-posed problem 15 (2007) 1.
Z. B. Xu & G. F. Roach, "``Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces"}, Journal of Mathematical Analysis and Applications, 1991
H. K. Xu, "``Inequalities in Banach spaces with applications", Nonlinear Analysis 12 (1991) 1127.
S. Reich and S. Sabach, "``Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces", Nonlinear Anal. 73 (2010) 122.
Copyright (c) 2019 Journal of the Nigerian Society of Physical Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.