Taiwanese Journal of Mathematics

SOME WEIGHTED OPIAL-TYPE INEQUALITIES ON TIME SCALES

H. M. Srivastava, Kuei-Lin Tseng, Shio-Jenn Tseng, and Jen-Chieh Lo

Full-text: Open access

Abstract

Motivated essentially by several recent investigations which claimed to have generalized, improved and extended such classical inequalities as the well-known Opial's inequality, here we establish some general weighted Opial-type inequalities on time scales. We also provide counterexamples, corrections and modifications of the aforementioned recent claims by Wong et al. [Taiwanese J. Math., 12 (2008), 463-471].

Article information

Source
Taiwanese J. Math., Volume 14, Number 1 (2010), 107-122.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405730

Digital Object Identifier
doi:10.11650/twjm/1500405730

Mathematical Reviews number (MathSciNet)
MR2603445

Zentralblatt MATH identifier
1190.26027

Subjects
Primary: 26D15: Inequalities for sums, series and integrals 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 26-99

Keywords
Opial's inequality extremal functions Hölder's inequality time scales $rd$-continuous functions delta differentiability absolute continuity extremal functions

Citation

Srivastava, H. M.; Tseng, Kuei-Lin; Tseng, Shio-Jenn; Lo, Jen-Chieh. SOME WEIGHTED OPIAL-TYPE INEQUALITIES ON TIME SCALES. Taiwanese J. Math. 14 (2010), no. 1, 107--122. doi:10.11650/twjm/1500405730. https://projecteuclid.org/euclid.twjm/1500405730


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