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Piecewise Continuous Stepanov-Like Almost Automorphic Functions with Applications to Impulsive Systems

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author

Listed:
  • Syed Abbas

    (Indian Institute of Technology Mandi, School of Basic Sciences)

  • Lakshman Mahto

    (Indian Institute of Information Technology Dharwad, Department of Mathematics)

Abstract

In this chapter, we discuss Stepanov-like almost automorphic function in the framework of impulsive systems. Next, we establish the existence and uniqueness of such solution of a very general class of delayed model of impulsive neural network. The coefficients and forcing term are assumed to be Stepanov-like almost automorphic in nature. Since the solution is no longer continuous, so we introduce the concept of piecewise continuous Stepanov-like almost automorphic function. We establish some basic and important properties of these functions and then prove composition theorem. Composition theorem is an important result from the application point of view. Further, we use composition result and fixed point theorem to investigate existence, uniqueness and stability of solution of the problem under consideration. Finally, we give a numerical example to illustrate our analytical findings.

Suggested Citation

  • Syed Abbas & Lakshman Mahto, 2019. "Piecewise Continuous Stepanov-Like Almost Automorphic Functions with Applications to Impulsive Systems," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 119-140, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_4
    DOI: 10.1007/978-3-030-15242-0_4
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