Shi, D.; Farid, G.; Younis, B.A.I.; Abu-Zinadah, H.; Anwar, M. A Unified Representation of Q- and h-Integrals and Consequences in Inequalities. Axioms 2024, 13, 278, doi:10.3390/axioms13040278.
Shi, D.; Farid, G.; Younis, B.A.I.; Abu-Zinadah, H.; Anwar, M. A Unified Representation of Q- and h-Integrals and Consequences in Inequalities. Axioms 2024, 13, 278, doi:10.3390/axioms13040278.
Shi, D.; Farid, G.; Younis, B.A.I.; Abu-Zinadah, H.; Anwar, M. A Unified Representation of Q- and h-Integrals and Consequences in Inequalities. Axioms 2024, 13, 278, doi:10.3390/axioms13040278.
Shi, D.; Farid, G.; Younis, B.A.I.; Abu-Zinadah, H.; Anwar, M. A Unified Representation of Q- and h-Integrals and Consequences in Inequalities. Axioms 2024, 13, 278, doi:10.3390/axioms13040278.
Abstract
This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are 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 by using the concept of q−h-derivative/q−h-integral.
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