Some new deterministic and random variational inequalities and their applications

A non-compact deterministic variational inequality which is used to prove an existence theorem for saddle points in the setting of topological vector spaces and a random variational inequality. The latter result is then applied to obtain the random version of the Fan's best approximation theorem. Several random fixed point theorems are obtained as applications of the random best approximation theorem.

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Best Approximation and Fixed Point Theorems for Set-Valued Mappings in Topological Vector Spaces

Topological Methods for Set-Valued Nonlinear Analysis ◽

10.1142/9789812791467_0006 ◽

2008 ◽

pp. 447-461

Keyword(s):

Fixed Point ◽

Best Approximation ◽

Fixed Point Theorems ◽

Vector Spaces ◽

Topological Vector Spaces ◽

Set Valued Mappings

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Fixed point theorems in topological vector spaces and applications to random normed spaces

Fixed Point Theory in Probabilistic Metric Spaces ◽

10.1007/978-94-017-1560-7_6 ◽

2001 ◽

pp. 205-244

Author(s):

Olga Hadžić ◽

Endre Pap

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Vector Spaces ◽

Normed Spaces ◽

Topological Vector Spaces ◽

Random Normed Spaces

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Common fixed point theorems and minimax inequalities in locally convex Hausdorff topological vector spaces

Applicable Analysis ◽

10.1080/00036810903331874 ◽

2009 ◽

Vol 88 (12) ◽

pp. 1691-1699 ◽

Cited By ~ 6

Author(s):

Ravi P. Agarwal ◽

Mircea Balaj ◽

Donal O'Regan

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Vector Spaces ◽

Minimax Inequalities ◽

Topological Vector Spaces ◽

Locally Convex ◽

Common Fixed Point Theorems

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Fixed point theorems for condensing admissible maps in topological vector spaces

Archiv der Mathematik ◽

10.1007/s00013-003-0477-x ◽

2003 ◽

Vol 80 (3) ◽

pp. 319-330

Author(s):

In-Sook Kim

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Vector Spaces ◽

Topological Vector Spaces ◽

Admissible Maps

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Some fixed point theorems in topological vector spaces

Demonstratio Mathematica ◽

10.1515/dema-1996-0312 ◽

1996 ◽

Vol 29 (3) ◽

Author(s):

Ismat Beg ◽

Abdul Latif ◽

Tahira Yasmeen Minhas

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Vector Spaces ◽

Topological Vector Spaces

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Vector and Ordered Variational Inequalities and Applications to Order-Optimization Problems on Banach Lattices

Journal of Applied Mathematics ◽

10.1155/2013/439394 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Linsen Xie ◽

Jinlu Li ◽

Wenshan Yang

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Variational Inequalities ◽

Fixed Point Theorems ◽

Optimization Problems ◽

Banach Lattices ◽

Variational Inequality Problems ◽

Vector Spaces ◽

Real Vector ◽

Finite Dimensional

We investigate the connections between vector variational inequalities and ordered variational inequalities in finite dimensional real vector spaces. We also use some fixed point theorems to prove the solvability of ordered variational inequality problems and their application to some order-optimization problems on the Banach lattices.

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FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES

Asian-European Journal of Mathematics ◽

10.1142/s1793557111000307 ◽

2011 ◽

Vol 04 (03) ◽

pp. 373-387 ◽

Cited By ~ 2

Author(s):

Ravi P. Agarwal ◽

Donal O'Regan ◽

Mohamed-Aziz Taoudi

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Vector Spaces ◽

Compact Sets ◽

Multivalued Maps ◽

Weakly Compact ◽

Topological Vector Spaces ◽

Admissible Maps ◽

Weakly Compact Sets ◽

Locally Convex

We present new fixed point theorems for multivalued [Formula: see text]-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

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