Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(5): 1023-1032

Printed September 1, 2011

https://doi.org/10.4134/BKMS.2011.48.5.1023

Copyright © The Korean Mathematical Society.

An Ekeland type variational principle on gauge spaces with applications to fixed point theory, drop theory and coercivity

Jong-Sook Bae, Seong-Hoon Cho, and Jeong-Jin Kim

Moyngji University, Hanseo University, Moyngji University

Abstract

In this paper, a new Ekeland type variational principle on gauge spaces is established. As applications, we give Caristi-Kirk type fixed point theorems on gauge spaces, and Dane\v{s}' drop theorem on semi-normed spaces. Also, we show that the Palais-Smale condition implies coercivity on semi-normed spaces.

Keywords: variational principle, gauge space, fixed point, drop theorem, Palais-Smale condition

MSC numbers: 54H25, 49J40, 49J45