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Abstract and Applied Analysis
Volume 2016, Article ID 1984874, 6 pages
Research Article

Quasi-Hyperbolicity and Delay Semigroups

1Department of Mathematics, University of Delhi, Delhi 110 007, India
2Department of Mathematics, University of Delhi, South Campus, Benito Juarez Road, New Delhi 110 021, India

Received 1 June 2016; Accepted 28 September 2016

Academic Editor: Jozef Banas

Copyright © 2016 Shard Rastogi and Sachi Srivastava. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study quasi-hyperbolicity of the delay semigroup associated with the equation , where is the history function and is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.