TY - JOUR AU - Wang, Hongjun AU - Zheng, Yuchun PY - 2016 TI - Fixed point theorem and nonlinear complementarity problem in Hilbert spaces JO - Journal of Nonlinear Sciences and Applications SP - 1957--1964 VL - 9 IS - 5 AB - In this paper, the concept of the strongly monotone type mapping is introduced, which contains the strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence between the fixed point problem and the complementarity problem of strongly monotone type mapping. Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution of such a nonlinear complementarity problem on the proper conditions. The error estimation of such an iteration is discussed. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.05.02 DO - 10.22436/jnsa.009.05.02 ID - Wang2016 ER - TY - JOUR TI - Nonexpansive projections on subsets of Banach spaces AU - R. E. Bruck JO - Pacific J. Math. PY - 1973 DA - 1973// VL - 47 ID - Bruck1973 ER - TY - JOUR TI - On fixed and periodic points under contractive mappings AU - M. Edelstein JO - J. London Math. Soc. PY - 1962 DA - 1962// VL - 37 ID - Edelstein 1962 ER - TY - JOUR TI - Engineering and Economic Applications of Complementarity Problems AU - M. C. Ferris AU - J. S. Pang JO - SIAM Rev. PY - 1997 DA - 1997// VL - 39 ID - Ferris1997 ER - TY - BOOK TI - Topics in metric fixed point theory AU - K. Goebel AU - W. A. Kirk PB - Cambridge University Press PY - 1990 DA - 1990// CY - Cambridge ID - Goebel1990 ER - TY - BOOK TI - Classical theory of nonexpansive mappings AU - K. Goebel AU - W. A. Kirk PB - Kluwer Acad. Publ. PY - 2001 DA - 2001// CY - Dordrecht ID - Goebel2001 ER - TY - JOUR TI - Fixed points of nonexpansive maps AU - B. Halpern JO - Bull. Amer. Math. Soc. PY - 1967 DA - 1967// VL - 73 ID - Halpern1967 ER - TY - JOUR TI - Finite-dimensional variational inequality and nonlinear complementarity problem: A survey of theory, algorithms and applications AU - P. T. Harker AU - J. S. Pang JO - Math. Programming PY - 1990 DA - 1990// VL - 48 ID - Harker1990 ER - TY - JOUR TI - Fixed points by a new iteration method AU - S. Ishikawa JO - Proc. Amer. Math. Soc. PY - 1974 DA - 1974// VL - 44 ID - Ishikawa 1974 ER - TY - JOUR TI - Fixed points and iteration of a nonexpansive mappings in Banach space AU - S. Ishikawa JO - Proc. Amer. Math. Soc. PY - 1976 DA - 1976// VL - 59 ID - Ishikawa 1976 ER - TY - JOUR TI - Two observations about the method of successive approximations AU - M. A. Krasnoselskii JO - Uspehi Math. Nauk PY - 1955 DA - 1955// VL - 10 ID - Krasnoselskii 1955 ER - TY - JOUR TI - Mean value methods in iteration AU - W. R. Mann JO - Proc. Amer. Math. Soc. PY - 1953 DA - 1953// VL - 4 ID - Mann 1953 ER - TY - JOUR TI - A nonlinear complementarity problem in mathematical programming in Hilbert space AU - S. Nanda JO - Bull. Austral. Math. Soc. PY - 1979 DA - 1979// VL - 20 ID - Nanda1979 ER - TY - JOUR TI - Equivalence of nonlinear complementarity problems and least-element problems in Banach lattices AU - R. C. Riddell JO - Math. Oper. Res. PY - 1981 DA - 1981// VL - 6 ID - Riddell1981 ER - TY - JOUR TI - On the equivalence of nonlinear complementarity problems and least-element problems AU - S. Schaible AU - J. C. Yao JO - Math. Programming PY - 1995 DA - 1995// VL - 70 ID - Schaible1995 ER - TY - JOUR TI - Halpern iteration for firmly type nonexpansive mappings AU - Y. Song AU - X. Chai JO - Nonlinear Anal. PY - 2009 DA - 2009// VL - 71 ID - Song2009 ER - TY - JOUR TI - Fixed point property and approximation of a class of nonexpansive mappings AU - Y. Song AU - Y. Huang AU - JO - Fixed Point Theory Appl. PY - 2014 DA - 2014// VL - 2014 ID - Song2014 ER - TY - JOUR TI - Successive approximations for quasi-firmly type nonexpansive mappings AU - Y. Song AU - Q. Li JO - Math. Commun. PY - 2011 DA - 2011// VL - 16 ID - Song2011 ER - TY - JOUR TI - The F-complementarity problem and its equivalence with the least element problem AU - H. Y. Yin AU - C. X. Xu AU - Z. X. Zhang JO - Acta Math. Sinica (Chin. Ser.) PY - 2001 DA - 2001// VL - 44 ID - Yin2001 ER - TY - JOUR TI - Equivalence of generalized mixed complementarity and generalized mixed least element problems in ordered spaces AU - L. C. Zeng AU - Q. H. Ansari AU - J. C. Yao JO - Optimization PY - 2009 DA - 2009// VL - 58 ID - Zeng2009 ER - TY - JOUR TI - A class of variational-like inequality problems and its equivalence with the least element problems AU - L. C. Zeng AU - J. C. Yao JO - J. Nonlinear Convex Anal. PY - 2005 DA - 2005// VL - 6 ID - Zeng2005 ER -