Strong convergence of an iterative algorithm involving nonlinear mappings of nonexpansive and accretive type

References

• Xu HK. Inequalities in Banach spaces with applications. Nonlinear Anal. 1991;16:1127–1138. doi: 10.1016/0362-546X(91)90200-K
   Web of Science ®Google Scholar
• Bruck RE. Nonexpansive projections on subsets of Banach spaces. Pacific J Math. 1973;47:341–355. doi: 10.2140/pjm.1973.47.341
   Web of Science ®Google Scholar
• Gobel K, Reich S. Uniform convexity, hyperbolic geometry and nonexpansive mappings. New York (NY): Marcel Dekker; 1984.
   Google Scholar
• Reich S. Asymptotic behavior of contractions in Banach spaces. J Math Anal Appl. 1973;44:57–70. doi: 10.1016/0022-247X(73)90024-3
   Web of Science ®Google Scholar
• Meir A, Keeler E. A theorem on contraction mappings. J Math Anal Appl. 1969;28:326–329. doi: 10.1016/0022-247X(69)90031-6
   Web of Science ®Google Scholar
• Browder FE. Nonexpansive nonlinear operators in a Banach space. Proc Natl Acad Sci USA. 1965;54:1041–1044. doi: 10.1073/pnas.54.4.1041
   PubMed Web of Science ®Google Scholar
• Kato T. Nonlinear semigroups and evolution equations. J Math Soc Japan. 1967;19:508–520. doi: 10.2969/jmsj/01940508
   Web of Science ®Google Scholar
• Bauschke HH, Borwein JM. On projection algorithms for solving convex feasibility problems. SIAM Rev. 1996;38:367–426. doi: 10.1137/S0036144593251710
   Web of Science ®Google Scholar
• Combettes PL. The convex feasibility problem in image recovery. Adv Imag Electron Phys. 1996;95:155–270. doi: 10.1016/S1076-5670(08)70157-5
   Google Scholar
• Cho SY, Li W, Kang SM. Convergence analysis of an iterative algorithm for monotone operators. J Inequal Appl. 2013;2013, Article ID 199.
   Web of Science ®Google Scholar
• Hieu DV, Moudafi A. A barycentric projected-subgradient algorithm for equilibrium problems. J Nonlinear Var Anal. 2017;1:43–59.
   Google Scholar
• Sahu DR, Yao J-C. A generalized hybrid steepest descent method and applications. J Nonlinear Var Anal. 2017;1:111–126.
   Google Scholar
• Shi LY, Ansari QH, Wen CF, et al. Incremental gradient projection algorithm for constrained composite minimization problems. J Nonlinear Var Anal. 2017;1:253–264.
   Web of Science ®Google Scholar
• Bin Dehaish BA, Qin X, Latif A, et al. Weak and strong convergence of algorithms for the sum of two accretive operators with applications. J Nonlinear Convex Anal. 2015;16:1321–1336.
   Web of Science ®Google Scholar
• Ceng LC, Wen CF, Yao Y. Iteration approaches to hierarchical variational inequalities for infinite nonexpansive mappings and finding zero points of m-accretive operators. J Nonlinear Var Anal. 2017;1:213–235.
   Google Scholar
• Kamimura S, Takahashi W. Weak and strong convergence of solutions to accretive operator inclusions and applications. Set-Valued Anal. 2000;8:361–374. doi: 10.1023/A:1026592623460
   Google Scholar
• Lv S. Convergence analysis of a Halpern-type iterative algorithm for zero points of accretive operators. Commun Optim Theory. 2016;2016, Article ID 16.
   Google Scholar
• Qin X, Yao J-C. Projection splitting algorithms for nonself operators. J Nonlinear Convex Anal. 2017;18:925–935.
   Web of Science ®Google Scholar
• Wei L, Agarwal RP. Relaxed iterative methods for an infinite family of d-accretive mappings in a Banach space and their applications. J Nonlinear Funct Anal. 2018;2018, Article ID 16.
   Google Scholar
• Barbu V. Nonlinear semigroups and differential equations in Banach space. Leyden: Noordhoff; 1976.
   Google Scholar
• Qin X, Cho SY, Wang L. Iterative algorithms with errors for zero points of m-accretive operators. Fixed Point Theory Appl. 2013;2013, Article ID 148.
   Google Scholar
• Mitrinovic DS. Analytic inequalities. New York (NY): Springer-Verlag; 1970.
   Google Scholar
• Aoyama K, Kimura Y, Takahashi W, et al. Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space. Nonlinear Anal. 2007;67:2350–2360. doi: 10.1016/j.na.2006.08.032
   Web of Science ®Google Scholar
• Suzuki T. Moudafi's viscosity approximations with Meir–Keeler contractions. J Math Anal Appl. 2007;325:342–352. doi: 10.1016/j.jmaa.2006.01.080
   Web of Science ®Google Scholar
• Browder FE, Petryshyn WV. Construction of fixed points of nonlinear mappings in Hilbert space. J Math Anal Appl. 1967;20:197–228. doi: 10.1016/0022-247X(67)90085-6
   Web of Science ®Google Scholar