[PDF] Top 20 Monotonicity rule for the quotient of two functions and its application

... foregoing monotonicity rules have been used very effectively in the study of special functions [–], differential geometry [, ], probability [] and approximation theory ...the monotonicity ... See full document

... the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric ...complete monotonicity properties for the functions involving the gamma ... See full document

... homogeneous functions, some monotonicity results for the ratio of two-parameter symmetric homogeneous functions are presented, which give an easier access to find two-parameter ... See full document

... [5] Ch.-P. Chen and F. Qi, Monotonicity results for the gamma function, J. Inequal. Pure Appl. Math. 3 (2003), no. 2, Art. 44. Available online at http://jipam.vu.edu.au/v4n2/065_02. html. RGMIA Res. Rep. Coll. 5 ... See full document

... converges for x ∈ [0, ∞ ). That is, a function f (x) is completely monotonic on x ∈ [0, ∞ ) if and only if it is a Laplace transform of a bounded and non-decreasing measure g(t). From the above theorem it follows that ... See full document

... [3] Ch.-P. Chen, F. Qi, P. Cerone and S. S. Dragomir, Monotonicity of sequences involving convex and concave functions, Math. Inequal. Appl. 6 (2003), no. 2, 229–239. RGMIA Res. Rep. Coll. 5 (2002), no. 1, ... See full document

... Some monotonicity results and inequalities for the function Γ(x + λ)/Γ(x + 1) and the gamma function Γ(x) with usual notation, where x > 0 and 0 < λ < 1 is independent of x, have been studied by many ... See full document

... invex monotonicity, strictly pseudoinvex monotonicity, and quasi- invex ...pseudoinvex monotonicity and pseudoinvex monotonicity were ...pseudoinvex monotonicity were given by Yang et ... See full document

... tonta veotabilis Schäffer, a fresh brown cyst of H. cruciferae was found to have been perforated and a juvenile Hypogastrura sp. (probably denticulata Bagnall) was seen feeding on the cyst contents. In the same culture ... See full document

... Testing with two-sided error, however, does not require a dependence on k. In fact the problem has been well-studied in the machine learning literature in the context of testing/learning “union of intervals” [35, ... See full document

... invex functions have been introduced in the ...invex functions and applied it to the establishment of the sufficient optimality conditions and duality in (multi objective) non-linear ... See full document

... the rule of law and remain a stable ...of its territorial ...with its own security and related challenges such as its territorial disputes; it therefore needs as many regional allies as ... See full document

... We would like to mention that Qi et al. obtained many important achievements con- cerning the complete (logarithmic) monotonicity of the ratios of gamma and polygamma functions from  on, such as [, ... See full document

... Rifaximin, a virtually non-absorbed rifamycin drug is gaining attention for its broad-spectrum of activity. A couple of methods have been reported for its determination in biological matrices. However, ... See full document

... Remark 2.7.2. Except Wendel’s result, all inequalities above take values on N, the set of positive integers. In other words, only Wendel’s double inequality (2.6), the earliest result on this topic, takes values on (0, ... See full document

... a quotient space of strictly monotone continuous functions on a real interval and show that a new average function on this quotient space is ... See full document

... Our final result is based on the Chebyshev integral inequality [26, p. 40], which states the following: suppose f and g are two integrable functions and monotonic in the same sense (either both decreasing or ... See full document

... One of the prominent mathematical fea- tures of natural language is the prevalence of “upward” and “downward” inferences involving determiners and other functional expressions. These inferences are asso- ciated with ... See full document

... The aim of this paper is to establish the following Brunn-Minkowski type inequalities for dual mixed quermassintegral quotient functions of star bodies... Zhang et al.[r] ... See full document

... monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma ...q-Zeta Functions and Associated Series and ...of functions ... See full document