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Báo cáo hóa học: "Research Article Composition Theorems of Stepanov Almost Periodic Functions and Stepanov-Like Pseudo-Almost Periodic Functions"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Composition Theorems of Stepanov Almost Periodic Functions and Stepanov-Like Pseudo-Almost Periodic Functions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 654695 12 pages doi 10.1155 2011 654695 Research Article Composition Theorems of Stepanov Almost Periodic Functions and Stepanov-Like Pseudo-Almost Periodic Functions Wei Long and Hui-Sheng Ding College of Mathematics and Information Science Jiangxi Normal University Nanchang Jiangxi 330022 China Correspondence should be addressed to Hui-Sheng Ding dinghs@mail.ustc.edu.cn Received 31 December 2010 Accepted 20 February 2011 Academic Editor Toka Diagana Copyright 2011 W. Long and H.-S. Ding. 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 establish a composition theorem of Stepanov almost periodic functions and with its help a composition theorem of Stepanov-like pseudo almost periodic functions is obtained. In addition we apply our composition theorem to study the existence and uniqueness of pseudo-almost periodic solutions to a class of abstract semilinear evolution equation in a Banach space. Our results complement a recent work due to Diagana 2008 . 1. Introduction Recently in 1 2 Diagana introduced the concept of Stepanov-like pseudo-almost periodicity which is a generalization of the classical notion of pseudo-almost periodicity and established some properties for Stepanov-like pseudo-almost periodic functions. Moreover Diagana studied the existence of pseudo-almost periodic solutions to the abstract semilinear evolution equation u f A t u t f t u t . The existence theorems obtained in 1 2 are interesting since f U is only Stepanov-like pseudo-almost periodic which is different from earlier works. In addition Diagana et al. 3 introduced and studied Stepanov-like weighted pseudo-almost periodic functions and their applications to abstract evolution equations. On the other hand due to the work of 4 by N Guerekata .