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Advances in Opial’s Type Integral Inequalities

In: Mathematics Without Boundaries

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  • Chang-Jian Zhao

    (China Jiliang University, Department of Mathematics)

  • Wing-Sum Cheung

    (The University of Hong Kong, Department of Mathematics)

Abstract

Opial’s inequality and its generalizations, extensions and discretizations play a fundamental role in the study of existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations. Over the years, Opial’s type integral inequalities have been receiving non-diminishing attention. In this article, we establish some new Opial’s type integral inequalities which in special cases yield some existing results of Rozanova, Agarwal-Pang, Pachpatte, Das and Agarwal-Sheng, and provide new and handy tools to qualitative as well as quantitative analysis of solutions to differential equations.

Suggested Citation

  • Chang-Jian Zhao & Wing-Sum Cheung, 2014. "Advances in Opial’s Type Integral Inequalities," Springer Books, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematics Without Boundaries, edition 127, pages 749-778, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1106-6_25
    DOI: 10.1007/978-1-4939-1106-6_25
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