• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.1-9
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• 2006

Based on the Schauder fixed point theorem, we give a Leray-Schauder type fixed point theorem for countably condensing mappings in a more general setting and apply it to obtain eigenvalue results on condensing mappings in a simple proof. Moreover, we present a generalization of Sadovskii's fixed point theorem for count ably condensing self-mappings due to S. J. Daher.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.113-120
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• 2001

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.565-578
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• 1999

In this paper some common fixed point theorems for pairs of condensing mappings in a Banach space are proved and applications are given to a pair of nonlinear first order ordinary differential equations in Banach spaces for proving the existence of common solution under suitable conditions.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.139-145
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• 2016

In this paper, some new fixed point theorems for condensing mappings are established based on a well known result of Petryshyn. We use several Leray-Schauder type conditions to prove new fixed point results. We also obtain generalizations of Altman's theorem and Petryshyn's theorem as well.