Monotonicity properties and functional inequalities for the Volterra and incomplete Volterra functions. (English) Zbl 1446.33009
Summary: In this paper we prove some monotonicity, log-convexity and log-concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Turán type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.
MSC:
| 33D05 | \(q\)-gamma functions, \(q\)-beta functions and integrals |
| 11M35 | Hurwitz and Lerch zeta functions |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 33B15 | Gamma, beta and polygamma functions |
| 33E99 | Other special functions |
Keywords:
Volterra function; incomplete Volterra function; functional inequalities; completely monotonic; log-convex functions; Turán type inequalitiesReferences:
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