| Title:
|
An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces (English) |
| Author:
|
Khan, M. S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
25-31 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
strongly smooth Banach space |
| Keyword:
|
mildly nonlinear complementarity problem |
| MSC:
|
46N10 |
| MSC:
|
47N10 |
| MSC:
|
49A10 |
| MSC:
|
49A29 |
| MSC:
|
49J10 |
| MSC:
|
49J40 |
| MSC:
|
65K10 |
| MSC:
|
90C33 |
| idZBL:
|
Zbl 0827.49004 |
| idMR:
|
MR1334411 |
| . |
| Date available:
|
2009-01-08T18:15:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118729 |
| . |
| Reference:
|
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| Reference:
|
[2] Browder F.E.: Nonlinear monotone operators and convex sets in Banach spaces.Bull. Amer. Math. Soc. 71 (1965), 780-785. Zbl 0138.39902, MR 0180882 |
| Reference:
|
[3] Edelstein M.: On nearest points of sets in uniformly convex Banach spaces.J. London Math. Soc. 43 (1968), 375-377. Zbl 0183.40403, MR 0226364 |
| Reference:
|
[3] Edelstein M.: On fixed and periodic points under contractive mappings.J. London Math. Soc. 37 (1962), 74-79. Zbl 0113.16503, MR 0133102 |
| Reference:
|
[5] Giles J.R.: Classes of semi-inner product spaces.Trans. Amer. Math. Soc. 129 (1967), 436-446. Zbl 0157.20103, MR 0217574 |
| Reference:
|
[6] Lumer G.: Semi-inner product spaces.Trans. Amer. Math. Soc. 100 (1969), 29-43. MR 0133024 |
| Reference:
|
[7] Nanda S.: A non-linear complementarity problem in semi-inner product space.Rendiconti di Matematica 1 (1982), 167-171. MR 0663723 |
| Reference:
|
[8] Nanda S., Nanda S.: On stationary points and the complementarity problem.Bull. Austral. Math. Soc. 21 (1980), 351-356. MR 0585193 |
| Reference:
|
[9] 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. MR 1041934 |
| Reference:
|
[10] Noor M.A.: On the non-linear complementarity problem.J. Math. Anal. Appl. 123 (1987), 455-460. |
| Reference:
|
[11] Noor M.A.: Mildly non-linear variational inequalities.Math. Anal. Numer. Theory Approx. 24 (1982), 99-110. MR 0692191 |
| Reference:
|
[12] Noor M.A.: Generalized quasi complementarity problems.J. Math. Anal. Appl. 120 (1986), 321-327. |
| . |
