Abstract Leray–Schauder Type Alternatives and Extensions

Donal O’Regan

doi:10.2478/auom-2019-0012

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Abstract Leray–Schauder Type Alternatives and Extensions

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 27 (2019): Issue 1 (March 2019)

By: Donal O’Regan

Open Access

|Mar 2019

Abstract

We present a Leray–Schauder type alternative for a general class of maps. This enables us to obtain some Birkhoff–Kellogg type results and a Furi–Pera result.

References

[1]. R.P Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001.10.1017/CBO9780511543005
Search in Google Scholar Back to article
[2]. R.P. Agarwal, D. O’Regan, Birkhoff–Kellogg theorems on invariant directions for multimaps, Abstract and Applied Analysis,2003:7(2003), 435–448.10.1155/S1085337503205030
Search in Google Scholar Back to article
[3]. R.P. Agarwal and D. O’Regan, Essential Ucκ$U_c^\kappa$-type maps and Birkhoff–Kellogg theorems, Journal of Applied Mathematics and Stochastic Analysis,2004:1(2004), 1–8.10.1155/S1048953304302017
Search in Google Scholar Back to article
[4]. X.P. Ding, W.K. Kim and K.K. Tan, A selection theorem and its applications, Bull. Austral. Math. Soc.,46(1992), 205–212.10.1017/S0004972700011849
Search in Google Scholar Back to article
[5]. G. Fournier and A. Granas, The Lefschetz fixed point theorem for some classes on non-metrizable spaces, J. Math. Pures Appl.,52(1973), 271–283.
Search in Google Scholar Back to article
[6]. M. Furi and P. Pera, A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals, Annales Polonici Mathematici,47(1987), 331–346.10.4064/ap-47-3-331-346
Search in Google Scholar Back to article
[7]. A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.10.1007/978-0-387-21593-8
Search in Google Scholar Back to article
[8]. D. O’Regan, Furi-Pera type theorems for the Ucκ$U_c^\kappa$-admissible maps of Park, Math. Proc. R. Ir. Acad.,102A(2002), 163–173.10.1353/mpr.2002.0012
Search in Google Scholar Back to article
[9]. D. O’Regan, A nonlinear alternative for maps with continuous selections, Communications in Applied Analysis,16(2012), 175–178.
Search in Google Scholar Back to article
[10]. S. Park, Generalized Leray–Schauder principles for condensing admissible multifunctions, Ann. Math. Pura Appl.,172(1997), 65–85.10.1007/BF01782607
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2019-0012 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 233 - 243

Submitted on: Apr 10, 2017

Accepted on: Jan 31, 2018

Published on: Mar 2, 2019

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Essential maps,

coincidence points,

nonlinear alternatives

Related subjects:

Mathematics,

General mathematics

© 2019 Donal O’Regan, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 27 (2019): Issue 1 (March 2019)