An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces
Khan, M. S.
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 25-31 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We prove a result for the existence and uniqueness of the solution for a class of mildly nonlinear complementarity problem in a uniformly convex and strongly smooth Banach space equipped with a semi-inner product. We also get an extension of a nonlinear complementarity problem over an infinite dimensional space. Our last results deal with the existence of a solution of mildly nonlinear complementarity problem in a reflexive Banach space.

Publié le : 1995-01-01
Classification:  46N10,  47N10,  49A10,  49A29,  49J10,  49J40,  65K10,  90C33 
@article{118729,
     author = {M. S. Khan},
     title = {An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {25-31},
     zbl = {0827.49004},
     mrnumber = {1334411},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118729}
}

Khan, M. S. An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 25-31. http://gdmltest.u-ga.fr/item/118729/

Bazaraa M.S.; Goode J.J.; Nashed M.Z. A nonlinear complementarity problem in mathematical programming in Banach spaces, Proc. Amer. Math. Soc. 35 (1972), 165-170. (1972) | MR 0300163

Browder F.E. Nonlinear monotone operators and convex sets in Banach spaces, Bull. Amer. Math. Soc. 71 (1965), 780-785. (1965) | MR 0180882 | Zbl 0138.39902

Edelstein M. On nearest points of sets in uniformly convex Banach spaces, J. London Math. Soc. 43 (1968), 375-377. (1968) | MR 0226364 | Zbl 0183.40403

Edelstein M. On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74-79. (1962) | MR 0133102 | Zbl 0113.16503

Giles J.R. Classes of semi-inner product spaces, Trans. Amer. Math. Soc. 129 (1967), 436-446. (1967) | MR 0217574 | Zbl 0157.20103

Lumer G. Semi-inner product spaces, Trans. Amer. Math. Soc. 100 (1969), 29-43. (1969) | MR 0133024

Nanda S. A non-linear complementarity problem in semi-inner product space, Rendiconti di Matematica 1 (1982), 167-171. (1982) | MR 0663723

Nanda S.; Nanda S. On stationary points and the complementarity problem, Bull. Austral. Math. Soc. 21 (1980), 351-356. (1980) | MR 0585193

Nath B.; Lal S.N.; Mukerjee R.N. A generalized non-linear complementarity problem in semi-inner product space, Indian J. Pure Appl. Math. 21:2 (1990), 140-143. (1990) | MR 1041934

Noor M.A. On the non-linear complementarity problem, J. Math. Anal. Appl. 123 (1987), 455-460. (1987)

Noor M.A. Mildly non-linear variational inequalities, Math. Anal. Numer. Theory Approx. 24 (1982), 99-110. (1982) | MR 0692191

Noor M.A. Generalized quasi complementarity problems, J. Math. Anal. Appl. 120 (1986), 321-327. (1986)