RIEMANN-STIELTJES INTEGRABILITY OF FINITE DISCONTINUOUS FUNCTIONS ON TIME SCALES

Vikuozonuo Sekhose, Hemanta Kalita, Hemen Bharali

DOI Number
https://doi.org/10.22190/FUMI230125036S
First page
559
Last page
575

Abstract


We establish the equivalence of the Riemann-Stieltjes $\Delta$-integral as defined in \cite{Delfim1, Delfim2} in terms of the Darboux sum definition and the Riemann sum definition, and provide the definition of the Riemann-Stieltjes $\nabla$-integral in terms of the Riemann sum definition and prove its equivalence with the Riemann-Stieltjes $\nabla$-integral as defined in \cite{Delfim1} in terms of the Darboux sum definition. We establish a few results concerning finite discontinuity.

Keywords

Riemann-Stieltjes Delta Integral, Riemann-Stieltjes Nabla Integral, Time Scale.

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References


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DOI: https://doi.org/10.22190/FUMI230125036S

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