참고문헌
- K. Aoyama, H. Iiduka and W. Takahashi, Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory Appl. 2006 (2006), Article ID 35390, 13 pages.
- F.E. Browder, Fixed point theorems for noncompact mappings in Hilbert spaces, Proc. Natl. Acad. Sci. USA 53 (1965), 1272-1276. https://doi.org/10.1073/pnas.53.6.1272
- F.E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math. 18 (1976), 78-81.
- R.E. Bruck, Jr., Properties of fixed point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 251-262. https://doi.org/10.1090/S0002-9947-1973-0324491-8
-
R.E. Bruck, Jr., A strongly convergent iterative method for the solution of 0
${\in}$ Ux for a maximal monotone operator U in Hilbert space, J. Math. Anal. Appl. 48 (1974), 114-126. https://doi.org/10.1016/0022-247X(74)90219-4 - S.S. Chang, H.W.J. Lee and C.K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007), 329-334. https://doi.org/10.1016/j.aml.2006.04.017
- L.C. Ceng and J.C. Yao, An extragradient-like approximation method for variational inequality problems and fixed point problems, Appl. Math. Comput. 190 (2007), 205-215. https://doi.org/10.1016/j.amc.2007.01.021
- L.C. Ceng, C.Y. Wang and J.C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Methods Oper. Res. 67 (2008), 375-390. https://doi.org/10.1007/s00186-007-0207-4
- I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Academic Publ., Dordrecht, 1990.
- C.E. Chidume and H. Zegeye, Approximation methods for nonlinear operator equations, Proc. Amer. Math. Soc. 131 (2003), 2467-2478. https://doi.org/10.1090/S0002-9939-02-06769-2
-
Z. Huang and M.A. Noor, An explicit projection method for a system of nonlinear variational inequalities with different
$({\gamma},r)-cocoercive$ mappings, Appl. Math. Comput. 190 (2007), 356-361. https://doi.org/10.1016/j.amc.2007.01.032 - H. Iiduka and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005), 341-350. https://doi.org/10.1016/j.na.2003.07.023
- S. Kitahara and W. Takahashi, Image recovery by convex combinations of sunny nonexpansive retractions, Topol. Methods Nonlinear Anal. 2 (1993), 333-342. https://doi.org/10.12775/TMNA.1993.046
-
M.O. Osilike, Iterative solution of nonlinear equations of the
${\Psi}-strongly$ accretive type, J. Math. Anal. Appl. 200 (1996), 259-271. https://doi.org/10.1006/jmaa.1996.0203 - X. Qin, S. M. Kang and M. Shang, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Anal. 87 (2008), 421-430. https://doi.org/10.1080/00036810801952953
- X. Qin, M. Shang and H. Zhou, Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces, Appl. Math. Comput. 200 (2008), 242-253. https://doi.org/10.1016/j.amc.2007.11.004
- S. Reich, Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl. 44 (1973), 57-70. https://doi.org/10.1016/0022-247X(73)90024-3
- S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292. https://doi.org/10.1016/0022-247X(80)90323-6
- T. Suzuki, Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl. 305 (2005), 227-239. https://doi.org/10.1016/j.jmaa.2004.11.017
- T. Suzuki, Moudafi's viscosity approximations with Meir-Keeler contractions, J. Math. Anal. Appl. 325 (2007), 342-352. https://doi.org/10.1016/j.jmaa.2006.01.080
- R.U. Verma, On a new system of nonlinear variational inequalities and associated iterative algorithms, Math. Sci. Res. Hot-Line 3 (1999), 65-68.
- R.U. Verma, Generalized class of partial relaxed monotonicity and its connections, Adv. Nonlinear Var. Inequal. 7 (2004), 155-164.
- R.U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (2004), 203-210. https://doi.org/10.1023/B:JOTA.0000026271.19947.05
- R.U. Verma, General convergence analysis for two-step projection methods and applications to variational problems, Appl. Math. Lett. 18 (2005), 1286-1292. https://doi.org/10.1016/j.aml.2005.02.026
- H.K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 1 (1991), 1127-1138.
- H.K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc. 66 (2002), 240-256. https://doi.org/10.1112/S0024610702003332
- Y. Yao and J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2007), 1551-1558. https://doi.org/10.1016/j.amc.2006.08.062
- H. Zhou, A characteristic condition for convergence of steepest descent approximation to accretive operator equations, J. Math. Anal. Appl. 271 (2002), 1-6. https://doi.org/10.1016/S0022-247X(02)00122-1
- H. Zhou, Y.J. Cho and S.M. Kang, Characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations, Comput. Math. Appl. 39 (2000), 1-11.