Monotonicity properties on k-digamma function and its related inequalities

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Monotonicity and inequalities for the gamma function

Some Operator Inequalities on Chaotic Order and Monotonicity of Related Operator Function

and Applied Analysis 3 Theorem 5. If A n ≫ A n−1 ≫ ⋅ ⋅ ⋅ ≫ A 2 ≫ A 1 ≫ B and r 1 , r 2 , . . . , r n ≥ 0 for a natural number n. For any fixed δ ≥ 0, let p 1 , p 2 , . . . , p n be satisfied by

Inequalities and monotonicity properties for zeros of Hermite functions

We study the variation of the zeros of the Hermite function Hλ(t) with respect to the positive real variable λ. We show that, for each nonnegative integer n, Hλ(t) has exactly n + 1 real zeros when n < λ ≤ n + 1 and that each zero increases from −∞ to ∞ as λ increases. We establish a formula for the derivative of a zero with respect to the parameter λ; this derivative is a completely monotonic ...

Inequalities and Monotonicity properties for some special functions

The monotonicity, convexity, log-convexity and complete monotonicity properties for some special functions are proved, and some inequalities are established.