Constantin's inequality for nabla and diamond-alpha derivative

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GÜVENİLİR A. F., Kaymakcalan B., Pelen N. N.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2015
  • Doi Number: 10.1186/s13660-015-0681-9
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Constantin's inequality, nabla differentiation, nabla integration, diamond-alpha differentiation, diamond-alpha integration, PERTURBED DIFFERENTIAL-EQUATIONS, TIME SCALES
  • Middle East Technical University Affiliated: Yes

Abstract

Calculus for dynamic equations on time scales, which offers a unification of discrete and continuous systems, is a recently developed theory. Our aim is to investigate Constantin's inequality on time scales that is an important tool used in determining some properties of various dynamic equations such as global existence, uniqueness and stability. In this paper, Constantin's inequality is investigated in particular for nabla and diamond-alpha derivatives.