Approximation of Solutions of Nonlinear Equations of Monotone and Hammerstein Type

References

• Alber , Ya. 1986 . Iterative regularization in Banach spaces . Soviet Math. , 30 : 1 – 8 .
   Google Scholar
• Alber , Ya. , Iusem , A. and Solodov , M. 1997 . Minimization of nonsmooth convex functionals in Banach spaces . Journal of Convex Analysis , 4 : 235 – 254 .
   Google Scholar
• Alber , Ya. and Notik , A. 1984 . Geometric properties of Banach spaces and approximation methods of solutions of nonlinear operator equations . Soviet Math. Dokl. , 29 : 611 – 615 .
   Google Scholar
• Alber , Ya. and Notic , A.I. 1994 . On the iterative method for variational inequalities with nonsmooth unbounded operators in Banach space . J. Math. Anal. App1. , 188 : 928 – 939 .
   Web of Science ®Google Scholar
• Brézis , H. and Browder , F.E. 1974 . Some new results about Hammerstein equations . Bull. Amer. Math. Soc. , 80 : 567 – 572 .
   Web of Science ®Google Scholar
• Brezis , H. and Browder , F.E. 1975 . Existence theorems for nonlinear integral equations of Hammerstein type . Bull. Amer. Math. Soc. , 81 : 73 – 78 .
   Web of Science ®Google Scholar
• Browder , F.E. , de Figueiredo , D.G. and Gupta , P. 1970 . Maximal monotone operators and a nonlinear integral equations of Hammerstein type . Bull. Amer. Math. Soc. , 76 : 700 – 705 .
   Web of Science ®Google Scholar
• Browder , F.E. and Gupta , P. 1969 . Monotone operators and nonlinear integral equations of Hammerstein type . Bull. Amer. Math. Soc. , 75 : 1347 – 1353 .
   Web of Science ®Google Scholar
• Chang , S.-S. 1997 . On Chidume’s open questions and approximation solutions of multi-valued strongly accretive mapping equations in Banach spaces . J. Math. Anal. Appl. , 216 : 94 – 111 .
   Web of Science ®Google Scholar
• Chepanovich , R.Sh. 1984 . Nonlinear Hammerstein equations and fixed points . Publ. Inst. Math. (Beograd) N. S. , 35 : 119 – 123 .
   Google Scholar
• Chidume , C.E. 1986 . The iterative solution of the equation f ∈ x + Tx for a monotone operator T in Lp spaces . J. Math. Anal. Appl. , 116 : 531 – 537 .
   Web of Science ®Google Scholar
• Chidume , C.E. 1989 . Fixed point iterations for nonlinear Hammerstein equations involving nonexpansive and accretive mappings . Indian J. Pure Appl. Math. , 120 : 129 – 135 .
   Google Scholar
• Chidume , C.E. 1998 . Global iteration schemes for strongly pseudo-contractive maps . Proc. Amer. Math. Soc. , 126 : 2641 – 2649 .
   Web of Science ®Google Scholar
• Chidume , C.E. 1998 . Iterative solution of nonlinear equations of strongly accretive type . Math. Nachr. , 189 : 49 – 60 .
   Web of Science ®Google Scholar
• Chidume , C.E. Picard Iteration for Strongly Accretive and Strongly Pseudocontractive Lipschitz Maps to appear in: Nonlinear Analysis & Applications , Edited by: Agarwal , R.P. and O’Reagan , D. Kluwer Academic Publishers .
   Google Scholar
• Chidume , C.E. and Moore , C. 1999 . Fixed point iterations for pseudocontractive maps . Proc. Amer. Math. Soc. , 127 : 1163 – 1170 .
   Web of Science ®Google Scholar
• Chidume , C.E. and Moore , C. 2000 . Steepest descent method for equilibrium points of nonlinear systems with accretive operators . J. Math. Anal. Appl. , 245 : 142 – 160 .
   Web of Science ®Google Scholar
• Chidume , C.E. and Osilike , M.O. 2000 . Equilibrium points for a system involving m-accretive operators . Proc. Edinburgh Math. Soc. , 3 : 1 – 14 .
   Google Scholar
• Chidume , C.E. and Zegeye , H. 1999 . Approximation of the zeros of nonlinear m-Accretive operators . Nonlinear Analysis , 37 : 81 – 96 .
   Web of Science ®Google Scholar
• Chidume , C.E. and Zegeye , H. 2001 . Global iterative schemes for accretive operators . J. Math. Anal. Appl. , 257 : 364 – 377 .
   Web of Science ®Google Scholar
• Chidume , C.E. , Zegeye , H. and Ntatin , B. 1999 . A generalized steepest descent approximation for the zeros of m-accretive operators . J. Math. Anal. Appl. , 236 : 48 – 73 .
   Web of Science ®Google Scholar
• De Figueiredo , D.G. and Gupta , C.P. 1973 . On the variational method for the existence of solutions to nonlinear equations of Hammerstein type . Proc. Amer. Math. Soc. , 40 : 470 – 476 .
   Web of Science ®Google Scholar
• Deng , L. 1993 . On Chidume’s open questions . J. Math. Anal.Appl. , 174 : 441 – 449 .
   Web of Science ®Google Scholar
• Dolezale , V. 1979 . “ Monotone operators and its applications in automation and network theory ” . In Studies in Automation and Control , Vol. 3 , New York : Elsevier Science Publ .
   Google Scholar
• Figiel , T. 1976 . On the moduli of convexity and smoothness . Studia Mathematica , 56 : 121 – 155 .
   Web of Science ®Google Scholar
• Hammerstein , A. 1930 . Nichtlineare integralgleichungen nebst anwendungen . Acta Math. Soc. , 54 : 117 – 176 .
   Google Scholar
• Ishikawa , S. 1974 . Fixed points by a new iteration method . Proc. Amer. Math. Soc. , 44 : 147 – 150 .
   Web of Science ®Google Scholar
• Kacurovskii . 1960 . On monotone operators and convex functionals . Uspekhi Mat. Nauk , 15 : 213 – 215 .
   Google Scholar
• Lindenstrauss , J. and Tzafriry , L. 1979 . Classical Banach Spaces II , New York : Springer Verlag, Berlin-Heidelberg .
   Google Scholar
• Liu , L. 1997 . Approximation of fixed points of a strictly pseudocontractive mapping . Proc. Amer. Math. Soc. , 125 : 1363 – 1366 .
   Web of Science ®Google Scholar
• Mann , W.R. 1953 . Mean value methods in iteration . Proc. Amer. Math. Soc. , 4 : 506 – 510 .
   Web of Science ®Google Scholar
• Minty , G.J. 1962 . Monotone operators in Hilbert spaces . Duke Math. J. , 29 : 341 – 346 .
   Web of Science ®Google Scholar
• Pascali , D. and Sburlan . 1978 . Nonlinear Mappings of Monotone Type , Romania : Editura academiae, Bucaresti .
   Google Scholar
• Petryshyn , W.V. 1970 . Nonlinear equations involving non-compact operators . Proc. Amer. Math. Soc. Sympos. Pure Math. , 18 ( Part 1 ) : 206 – 233 . Providence, R.I
   Google Scholar
• Qihou , L. 1992 . A convergence theorem for Ishikawa iterates of continuous generalized nonexpansive maps . J. Math. Anal. Appl. , 165 : 305 – 309 .
   Web of Science ®Google Scholar
• Rhoades , B.E. 1994 . Fixed point iterations for certain nonlinear mappings . J. Math. Anal. Appl. , 183 : 118 – 120 .
   Web of Science ®Google Scholar
• Schu , J. 1991 . On a theorem of C.E. Chidume concerning the iterative approximation of fixed points . Math. Nachr. , 153 : 313 – 319 .
   Web of Science ®Google Scholar
• Tan , K.-K. and Xu , H.-K. 1993 . Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process . J. Math. Anal. Appl. , : 301 – 308 .
   Web of Science ®Google Scholar
• Vainberg , M.M. and Kacurovskii , R.I. 1959 . On the variational theory of nonlinear operators and equations . Dokl. Akad. Nauk , 129 : 1199 – 1202 .
   Web of Science ®Google Scholar
• Weng , X.L. 1991 . Fixed point iteration for local strictly pseudocontractive mappings . Proc. Amer. Math. Soc. , 113 : 727 – 731 .
   Web of Science ®Google Scholar
• Xu , H.K. 1991 . Inequalities in Banach spaces with applications . Nonlinear Analysis , 16 : 1127 – 1138 .
   Web of Science ®Google Scholar
• Xu , Z.B. and Roach , G.F. 1991 . Characteristic inequalities for uniformly convex and uniformly smooth Banach spaces . J. Math. Anal. Appl. , 157 : 189 – 210 .
   Web of Science ®Google Scholar
• Zarantonello , E.H. 1960 . Solving Functional Equations by Contractive Averaging , Madison : Mathematics Research Center Rep, #160, Mathematics Research Centre, Univesity of Wisconsin .
   Google Scholar