Assembling classical and dynamic inequalities accumulated on calculus of time scales. (English) Zbl 1474.26133

Sahir, Muhammad Jibril Shahab

Vestn. KRAUNTS, Fiz.-Mat. Nauki 33, No. 4, 26-36 (2020).

Summary: 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.

MSC:

26D15	Inequalities for sums, series and integrals
26A33	Fractional derivatives and integrals
26E70	Real analysis on time scales or measure chains

Keywords:

time scales; fractional Riemann-Liouville integral; Renyi inequality; Lyapunov inequality; Radon inequality

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