IJPAM: Volume 78, No. 6 (2012)

FIXED POINT AND MAXIMAL ELEMENT THEOREMS WITH
APPLICATIONS TO GENERALIZED ABSTRACT ECONOMIES

A.K. Dubey$^1$, A. Narayan$^2$
Department of Mathematics
Bhilai Institute of Technology
Bhilai House, Durg, Chattisgarh, 491001, INDIA


Abstract. In this paper, we establish some maximal element theorems for the $\Phi$-condensing multivalued maps in the setting of socio-economy or techno-economy spaces. As applications of our results, we obtain some general equilibrium existence theorems in the generalized abstract socio-economics with preference correspondences.

Received: March 12, 2012

AMS Subject Classification: 91B02, 52A07, 47H10

Key Words and Phrases: fixed point theorems, maximal element theorems, $\Phi$-condensing multivalued maps, transfer compactly open valued maps, generalized abstract economies

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 6