Axioms (Apr 2024)

A Unified Representation of <i>q</i>- and <i>h</i>-Integrals and Consequences in Inequalities

  • Da Shi,
  • Ghulam Farid,
  • Bakri Adam Ibrahim Younis,
  • Hanaa Abu-Zinadah,
  • Matloob Anwar

DOI
https://doi.org/10.3390/axioms13040278
Journal volume & issue
Vol. 13, no. 4
p. 278

Abstract

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This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called q−h-derivative/q−h-integral. These notions are further extended on the finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities for q−h-integrals are studied and directly connected with well known results in diverse fields of science and engineering. The theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified using the q−h-derivative/q−h-integral concept.

Keywords