MATHEMATICS

Assembling classical and dynamic inequalities accumulated on calculus of time scales

M. J. Sahir

Department of Mathematics, University of Sargodha, Sub-Campus Bhakkar

Abstract: In this paper, we present an extension of dynamic Renyi's inequality on time scales by using the time scale Riemann–Liouville type fractional integral. Furthermore, we find generalizations of the well–known Lyapunov's inequality and Radon's inequality on time scales by using the time scale Riemann–Liouville type fractional integrals. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues.

Keywords: time scales, fractional Riemann–Liouville integral, Renyi's inequality, Lyapunov's inequality, Radon's inequality.

UDC: 519.644

MSC: Primary 26D15; Secondary 26D20, 34N05

Language: English

DOI: 10.26117/2079-6641-2020-33-4-26-36