Complete Monotonicity of a Function Involving the (P, K)-Digamma Function

2018 ◽  
Vol 11 (2) ◽  
pp. 103-108 ◽  
Author(s):  
Li Yin
Keyword(s):  
Complete Monotonicity ◽  
Digamma Function

scholarly journals Extension of complete monotonicity results involving the digamma function

2018 ◽  
Vol 4 (2) ◽  
pp. 207-212
Author(s):  
Kwara Nantomah
Keyword(s):  
Analytical Techniques ◽  
Monotonicity Property ◽  
Complete Monotonicity ◽  
Digamma Function ◽  
Special Cases ◽  
Monotonicity Results

AbstractBy using some analytical techniques, we prove a complete monotonicity property of a certain function involving the (p, k)-digamma function. Subsequently, we derive some inequalities for the (p, k)- digamma function. As special cases of the established results, we deduce some new results concerning the p-digamma and the k-digamma functions. Our results are extensions of some previous results due to Qiu and Vuorinen, Mortici, and Merovci.

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

scholarly journals New fractional approaches for n-polynomial P-convexity with applications in special function theory

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu-Bo Chen ◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Special Functions ◽  
Real Life ◽  
Fractional Integrals ◽  
Digamma Function ◽  
Novel Approach ◽  
Inequality Theory ◽  
New Strategy ◽  
Significant Mechanism

Abstract Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues with high proficiency. This manuscript contributes to a captivating association of fractional calculus, special functions and convex functions. The authors develop a novel approach for investigating a new class of convex functions which is known as an n-polynomial $\mathcal{P}$ P -convex function. Meanwhile, considering two identities via generalized fractional integrals, provide several generalizations of the Hermite–Hadamard and Ostrowski type inequalities by employing the better approaches of Hölder and power-mean inequalities. By this new strategy, using the concept of n-polynomial $\mathcal{P}$ P -convexity we can evaluate several other classes of n-polynomial harmonically convex, n-polynomial convex, classical harmonically convex and classical convex functions as particular cases. In order to investigate the efficiency and supremacy of the suggested scheme regarding the fractional calculus, special functions and n-polynomial $\mathcal{P}$ P -convexity, we present two applications for the modified Bessel function and $\mathfrak{q}$ q -digamma function. Finally, these outcomes can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem.

scholarly journals Complete monotonicity related to the k-polygamma functions with applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Li Yin ◽  
Jumei Zhang ◽  
XiuLi Lin
Keyword(s):  
Complete Monotonicity ◽  
Polygamma Functions

Some complete monotonicity properties for the -gamma function

2013 ◽  
Vol 219 (21) ◽  
pp. 10538-10547 ◽  
Author(s):  
V.B. Krasniqi ◽  
H.M. Srivastava ◽  
S.S. Dragomir
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Monotonicity Properties

scholarly journals Some combinatorial series identities associated with the Digamma function and harmonic numbers

2000 ◽  
Vol 13 (3) ◽  
pp. 101-106 ◽  
Author(s):  
Tsu-Chen Wu ◽  
Shih-Tong Tu ◽  
H.M. Srivastava
Keyword(s):  
Harmonic Numbers ◽  
Digamma Function

scholarly journals An integral representation, complete monotonicity, and inequalities of the Catalan numbers

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 575-587 ◽  
Author(s):  
Feng Qi ◽  
Xiao-Ting Shi ◽  
Fang-Fang Liu
Keyword(s):  
Integral Representation ◽  
Generating Function ◽  
Integral Formula ◽  
Cauchy Integral Formula ◽  
Catalan Numbers ◽  
Complete Monotonicity ◽  
Cauchy Integral ◽  
Complex Functions

In the paper, by virtue of the Cauchy integral formula in the theory of complex functions, the authors establish an integral representation for the generating function of the Catalan numbers in combinatorics. From this, the authors derive an alternative integral representation, complete monotonicity, determinantal and product inequalities for the Catalan numbers.

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