The split common fixed point problem for generalized demimetric mappings in two Banach spaces

References

• Takahashi W. The split common fixed point problem and the shrinking projection method in Banach spaces. J Convex Anal. 2017;24:1015–1028.
   Web of Science ®Google Scholar
• Lin C-N, Takahashi W. Weak convergence theorem for a finite family of demimetric mappings with variational inequality problems in a Hilbert space. J Nonlinear Convex Anal. 2017;18:553–564.
   Web of Science ®Google Scholar
• Takahashi W. The split common fixed point problem and strong convergence theorems by hybrid methods in two Banach spaces. J Nonlinear Convex Anal. 2016;17:1051–1067.
   Web of Science ®Google Scholar
• Takahashi W. Strong convergence theorem for a finite family of demimetric mappings with variational inequality problems in a Hilbert space. Jpn J Ind Appl Math. 2017;34:41–57. doi: 10.1007/s13160-017-0237-0
   Web of Science ®Google Scholar
• Takahashi W, Wen C-F, Yao J-C. The shrinking projection method for a finite family of demimetric mappings with variational inequalty problems in a Hilbert space. Fixed Point Theory. 2018;19:407–419. doi: 10.24193/fpt-ro.2018.1.32
   Web of Science ®Google Scholar
• Kawasaki T, Takahashi W. A strong convergence theorem for countable families of nonlinear nonself mappings in Hilbert spaces and applications. J Nonlinear Convex Anal. 2018;19:543–560.
   Web of Science ®Google Scholar
• Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms. 1994;8:221–239. doi: 10.1007/BF02142692
   Google Scholar
• Byrne C, Censor Y, Gibali A, et al. The split common null point problem. J Nonlinear Convex Anal. 2012;13:759–775.
   Web of Science ®Google Scholar
• Censor Y, Segal A. The split common fixed-point problem for directed operators. J Convex Anal. 2009;16:587–600.
   Web of Science ®Google Scholar
• Moudafi A. The split common fixed point problem for demicontractive mappings. Inverse Probl. 2010;26:055007. 6 pp. doi: 10.1088/0266-5611/26/5/055007
   Web of Science ®Google Scholar
• Alsulami SM, Takahashi W. The split common null point problem for maximal monotone mappings in Hilbert spaces and applications. J Nonlinear Convex Anal. 2014;15:793–808.
   Web of Science ®Google Scholar
• Alsulami SM, Latif A, Takahashi W. Strong convergence theorems by hybrid methods for split feasibility problems in Hilbert spaces. J Nonlinear Convex Anal. 2015;16:2521–2538.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Algorithms for the split variational inequality problem. Numer Algorithms. 2012;59:301–323. doi: 10.1007/s11075-011-9490-5
   Web of Science ®Google Scholar
• Shehu Y, Mewomo OT. Further investigation into split common fixed point problem for demicontractive operators. Acta Math Sin (Engl Ser). 2016;32:1357–1376. doi: 10.1007/s10114-016-5548-6
   Web of Science ®Google Scholar
• Takahashi W, Xu H-K, Yao J-C. Iterative methods for generalized split feasibility problems in Hilbert spaces. Set-Valued Var Anal. 2015;23:205–221. doi: 10.1007/s11228-014-0285-4
   Web of Science ®Google Scholar
• Takahashi W. The split feasibility problem in Banach spaces. J Nonlinear Convex Anal. 2014;15:1349–1355.
   Web of Science ®Google Scholar
• Takahashi W. The split common null point problem in Banach spaces. Arch Math (Basel). 2015;104:357–365. doi: 10.1007/s00013-015-0738-5
   Web of Science ®Google Scholar
• Nakajo K, Takahashi W. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J Math Anal Appl. 2003;279:372–379. doi: 10.1016/S0022-247X(02)00458-4
   Web of Science ®Google Scholar
• Ohsawa S, Takahashi W. Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces. Arch Math (Basel). 2003;81:439–445. doi: 10.1007/s00013-003-0508-7
   Web of Science ®Google Scholar
• Solodov MV, Svaiter BF. Forcing strong convergence of proximal point iterations in a Hilbert space. Math Programming Ser A. 2000;87:189–202. doi: 10.1007/s101079900113
   Web of Science ®Google Scholar
• Takahashi W, Takeuchi Y, Kubota R. Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces. J Math Anal Appl. 2008;341:276–286. doi: 10.1016/j.jmaa.2007.09.062
   Web of Science ®Google Scholar
• Cioranescu I. Geometry of Banach spaces, duality mappings and nonlinear problems. Dordrecht: Kluwer; 1990.
   Google Scholar
• Reich S. Book review: geometry of Banach spaces, duality mappings and nonlinear problems. Bull Amer Math Soc. 1992;26:367–370. doi: 10.1090/S0273-0979-1992-00287-2
   Google Scholar
• Takahashi W. Nonlinear functional analysis. Yokohama: Yokohama Publishers; 2000.
   Google Scholar
• Takahashi W. Convex analysis and approximation of fixed points (Japanese). Yokohama: Yokohama Publishers; 2000.
   Google Scholar
• Browder FE. Nonlinear maximal monotone operators in Banach spaces. Math Ann. 1968;175:89–113. doi: 10.1007/BF01418765
   Web of Science ®Google Scholar
• Browder FE, Petryshyn WV. Construction of fixed points of nonlinear mappings in Hilbert spaces. J Math Anal Appl. 1967;20:197–228. doi: 10.1016/0022-247X(67)90085-6
   Web of Science ®Google Scholar
• Kocourek P, Takahashi W, Yao J-C. Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert space. Taiwanese J Math. 2010;14:2497–2511. doi: 10.11650/twjm/1500406086
   Web of Science ®Google Scholar
• Kohsaka F, Takahashi W. Existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces. SIAM J Optim. 2008;19:824–835. doi: 10.1137/070688717
   Web of Science ®Google Scholar
• Kohsaka F, Takahashi W. Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces. Arch Math (Basel). 2008;91:166–177. doi: 10.1007/s00013-008-2545-8
   Web of Science ®Google Scholar
• Takahashi W. Fixed point theorems for new nonlinear mappings in a Hilbert space. J Nonlinear Convex Anal. 2010;11:79–88.
   Web of Science ®Google Scholar
• Igarashi T, Takahashi W, Tanaka K. Weak convergence theorems for nonspreading mappings and equilibrium problems. In: Akashi S, Takahashi W, and Tanaka T, editors. Nonlinear analysis and optimization. Yokohama: Yokohama Publishers; 2008. p. 75–85.
   Google Scholar
• Takahashi W. Strong convergence theorems by hybrid methods for new demimetric mappings in Banach spaces. J Convex Anal. 2019;26, to appear.
   Web of Science ®Google Scholar
• Mosco U. Convergence of convex sets and of solutions of variational inequalities. Adv Math. 1969;3:510–585. doi: 10.1016/0001-8708(69)90009-7
   Web of Science ®Google Scholar
• Tsukada M. Convergence of best approximations in a smooth Banach space. J Approx Theory. 1984;40:301–309. doi: 10.1016/0021-9045(84)90003-0
   Web of Science ®Google Scholar
• Marino G, Xu H-K. Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J Math Anal Appl. 2007;329:336–346. doi: 10.1016/j.jmaa.2006.06.055
   Web of Science ®Google Scholar
• Takahashi W, Wong N-C, Yao J-C. Weak and strong mean convergence theorems for extended hybrid mappings in Hilbert spaces. J Nonlinear Convex Anal. 2011;12:553–575.
   Web of Science ®Google Scholar
• Takahashi W, Yao J-C, Kocourek P. Weak and strong convergence theorems for generalized hybrid nonself-mappings in Hilbert spaces. J Nonlinear Convex Anal. 2010;11:567–586.
   Web of Science ®Google Scholar
• Aoyama K, Kohsaka F, Takahashi W. Three generalizations of firmly nonexpansive mappings: their relations and continuous properties. J Nonlinear Convex Anal. 2009;10:131–147.
   Web of Science ®Google Scholar