General Opial Type Inequality for Quotient of Functions

Authors

  • Ana Barbir Faculty of Civil Engineering and Architecture, Split, Croatia
  • Kristina Kruli´c Himmelreich Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
  • Josip Peˇčarić Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia

DOI:

https://doi.org/10.5644/SJM.12.2.06

Keywords:

Opial inequality, Green function, Jensen inequality, Lidstone polynomial, Hermite interpolating polynomial

Abstract

In this paper we give the general Opial type inequality for quotient of functions. Our result contains two functions, convex and concave functions. We prove a new general inequality on a measure space $(\Omega,\Sigma,\mu)$. We apply our result to numerous symmetric functions and obtain new results that involve Green's functions, Lidstone series and the Hermite's interpolating polynomials.

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Published

30.05.2024

How to Cite

Barbir, A., Kruli´c Himmelreich, K., & Peˇčarić, J. (2024). General Opial Type Inequality for Quotient of Functions. Sarajevo Journal of Mathematics, 12(2), 193–204. https://doi.org/10.5644/SJM.12.2.06

Issue

Vol. 12 No. 2 (2016)

Section

Articles