• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.1021-1026
• /
• 2001

In this paper, we give an improvement of Carleman’s inequality by using the strict monotonicity of the power mean of n distinct positive numbers.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.125-135
• /
• 1998

In this paper we define the entropy rate and stationary Markov chain and we show the monotonicity of entropy per element and prove that the random tree $T_n$ grows linearly with n.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.1
• /
• pp.61-71
• /
• 1998

Petrov-Galerkin method is investigated for solving nonlinear systems without monotonicity. A monotone iteration is provided for solving the resulting problem. The numerical results show the advantages of such method.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1845-1856
• /
• 2016

In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some $Tur{\acute{a}}n$ type inequalities are deduced.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.575-598
• /
• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.225-242
• /
• 2017

A family of $Ap{\acute{e}}ry$-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.

• East Asian mathematical journal
• /
• v.27 no.5
• /
• pp.545-555
• /
• 2011

Based on the A-maximal(m)-relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong convergence results on proximal point algorithms in real Hilbert space settings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of variational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to first- order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for finding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.

• International Journal of Contents
• /
• v.12 no.2
• /
• pp.42-48
• /
• 2016

We present efficient algorithms for computing centroid directions for each of the three types of monotonicity in a polyhedron: strong, weak, and directional monotonicity, which can be used for optimizing directions in many 3D manufacturing processes. Strongly- and directionally-monotone directions are the poles of great circles separating a set of spherical polygons on the unit sphere, the centroids of which are shown to be obtained by applying the previous result for determining the maximum intersection of the set of their dual spherical polygons. Especially in this paper, we focus on developing an efficient method for approximating the weakly-monotone centroid, which is the pole of one of the great circles intersecting a set of spherical polygons on the unit sphere. The original problem is approximately reduced into computing the intersection of great bands for avoiding complicated computational complexity of non-convex objects on the unit sphere, which can be realized with practical linear-time operations.

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1261-1278
• /
• 2019

It is well-known that if ${\phi}^{{\prime}{\prime}}$ > 0 for all x, ${\phi}(0)=0$, and ${\phi}/x$ is interpreted as ${\phi}^{\prime}(0)$ for x = 0, then ${\phi}/x$ increases for all x. This has been extended in [Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions, J. Math. Anal. Appl. 336 (2007), 812-822]. In this paper, we extend the above result to the very general cases, and then use it to prove some (logarithmically) completely monotonic functions related to the gamma function. We also establish some inequalities for the gamma function and generalize some known results.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.987-998
• /
• 2015

In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of the Bernoulli numbers of the second kind.