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

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

Some fixed point theorems in topological vector spaces

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

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

2011 ◽  
Vol 04 (03) ◽  
pp. 373-387 ◽  
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.

scholarly journals Some new deterministic and random variational inequalities and their applications

1995 ◽  
Vol 8 (4) ◽  
pp. 381-391 ◽  
Author(s):  
Xian-Zhi Yuan ◽  
Jean-Marc Roy
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Best Approximation ◽  
Fixed Point Theorems ◽  
Approximation Theorem ◽  
Saddle Points ◽  
Vector Spaces ◽  
Random Fixed Point ◽  
Topological Vector Spaces ◽  
Random Variational Inequalities

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.

ON MODULATED TOPOLOGICAL VECTOR SPACES AND APPLICATIONS

2019 ◽  
Vol 101 (2) ◽  
pp. 325-332 ◽  
Author(s):  
WOJCIECH M. KOZLOWSKI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Modular Function ◽  
Function Spaces ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Modular Function Spaces ◽  
Bare Minimum ◽  
Minimalist Framework

We introduce a notion of modulated topological vector spaces, that generalises, among others, Banach and modular function spaces. As applications, we prove some results which extend Kirk’s and Browder’s fixed point theorems. The theory of modulated topological vector spaces provides a very minimalist framework, where powerful fixed point theorems are valid under a bare minimum of assumptions.

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