On an Inequality for the Ratio of Gamma Functions
نویسندگان
چکیده
The following inequality relating to the ratio of the gamma functions α logx x− Γ(x) Γ ( x+ x ) , where α is a suitable constant, is established for every x > 0 . This inequality gives a contribution to the recent results, proved by several authors, involving the functions Γ(x) and Γ ( 1 x ) . It also gives an alternative proof of a conjecture formulated by D. Kershaw and recently proved by G.J.O. Jameson and T.P. Jameson [5]. Mathematics subject classification (2010): 33B15, 26D07.
منابع مشابه
Hermite-Hadamard inequality for geometrically quasiconvex functions on co-ordinates
In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.
متن کاملBounds for the Ratio of Two Gamma Functions-from Wendel's and Related Inequalities to Logarithmically Completely Monotonic Functions
In the survey paper, along one of several main lines of bounding the ratio of two gamma functions, the authors retrospect and analyse Wendel’s double inequality, Kazarinoff’s refinement of Wallis’ formula, Watson’s monotonicity, Gautschi’s double inequality, Kershaw’s first double inequality, and the (logarithmically) complete monotonicity results of functions involving ratios of two gamma or q...
متن کاملOn the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications
In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.
متن کاملAn inequality related to $eta$-convex functions (II)
Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.
متن کاملComments on relaxed $(gamma, r)$-cocoercive mappings
We show that the variational inequality $VI(C,A)$ has aunique solution for a relaxed $(gamma , r)$-cocoercive,$mu$-Lipschitzian mapping $A: Cto H$ with $r>gamma mu^2$, where$C$ is a nonempty closed convex subset of a Hilbert space $H$. Fromthis result, it can be derived that, for example, the recentalgorithms given in the references of this paper, despite theirbecoming more complicated, are not...
متن کامل