Fixed point theorems for a class of maps in normed Boolean vector spaces

In this paper, without assuming the normalities of cones, we prove some new fixed point theorems of order-Lipschitz mappings restricted with linear bounded mappings in normed vector space in the framework of w-convergence via the method of upper and lower solutions. It is worth mentioning that the unique existence result of fixed points in this paper, presents a characterization of Picard-completeness of order-Lipschitz mappings.

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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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