A note on Weyl pseudo almost automorphic functions and their properties

被引：16
作者：
Syed Abbas
机构：
[1] School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175001, Himachal Pradesh
来源：
Mathematical Sciences | 2012年 / 6卷 / 1期
关键词：
34K14; 42A75; Almost automorphic functions; Weyl almost automorphic functions;
D O I：
10.1186/2251-7456-6-29
中图分类号：
学科分类号：
摘要：
Purpose: In this paper we discuss the notion of Weyl pseudo almost automorphic functions. These kind of functions are more general than almost automorphic functions and Stepanov almost automorphic functions. We establish the composition theorem for this class of functions. Methods: The Weyl norm has been used to prove the results. In order to prove the composition theorem, the function has been broken into different parts. Results: The concept of Weyl pseudo almost automorphic functions are defined. The composition theorem has been proved for this kind of functions. Conclusion: The concept is new and may be useful in the qualitative theory of differential equations. © 2012, Abbas; licensee Springer.
引用
收藏
相关论文
共 13 条
  • [1] Bohr H., Zur Theorie der Fastperiodischen Funktionen I, Acta, Math, 45, pp. 29-127, (1925)
  • [2] Zhang C.Y., Pseudo almost periodic solutions of some differential equations, J. Math. Anal. Appl, 181, 1, pp. 62-76, (1994)
  • [3] Diagana T., Weighted pseudo almost periodic functions and applications, Compt. Rendus. Math, 343, 103, pp. 643-646, (2006)
  • [4] Bochner S., von Neumann J., On compact solutions of operational-differential equations, I. Annals of Mathematics, 36, 1, pp. 255-291, (1935)
  • [5] N'Guerekata G.M., Topics in Almost Automorphy, (2005)
  • [6] Liang J., Zhang J., Xiao T.J., Composition of pseudo almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl, 340, 2, pp. 1493-1499, (2008)
  • [7] Blot J., Mophu G.M., N'Guerekata G.M., Pennequin D., Weighted pseudo almost automorphic functions and applications to abstract differential equations, Nonlinear Anal. TMA, 71, pp. 903-909, (2009)
  • [8] Abbas S., Weighted pseudo almost automorphic sequences and their applications, Electron J. Diff. Equ, 2010, 121, pp. 1-14, (2010)
  • [9] Weyl H., Integralgleichungen und fastperiodische Funktionen, Math Ann, 97, pp. 338-356, (1927)
  • [10] Diagana T., Stepanov-like pseudo almost periodic functions and their applications to differential equations, Comm. Math. Anal, 3, 1, pp. 9-18, (2007)
12