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We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic functions. It is shown that the sum of two quasinearly subharmonic functions may not be quasinearly subharmonic. Moreover, we characterize the harmonicity via quasinearly subharmonicity.
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of convexity on
For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely determined b
In this paper, we present a mixed-type integral-sum representation of the cylinder functions $mathscr{C}_mu(z)$, which holds for unrestricted complex values of the order $mu$ and for any complex value of the variable $z$. Particular cases of these re
This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.
The class of generating functions for completely monotone sequences (moments of finite positive measures on $[0,1]$) has an elegant characterization as the class of Pick functions analytic and positive on $(-infty,1)$. We establish this and another s