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Advances in Opial’s Type Integral Inequalities

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Mathematics Without Boundaries

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.

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Acknowledgements

C.-J. Zhao’s research was supported by the National Natural Sciences Foundation of China (11371334) and the Zhejiang Provincial Natural Science Foundation of China (Y13A010019). W.S. Cheung’s research was supported by a HKU Seed Grant for Basic Research.

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Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, 310018, Hangzhou, People’s Republic of China

    Chang-Jian Zhao

  2. Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    Wing-Sum Cheung

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  1. Chang-Jian Zhao
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  2. Wing-Sum Cheung
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Correspondence to Chang-Jian Zhao .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Dept. Industrial & Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Zhao, CJ., Cheung, WS. (2014). Advances in Opial’s Type Integral Inequalities. In: Rassias, T., Pardalos, P. (eds) Mathematics Without Boundaries. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1106-6_25

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