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Superstability of Pexiderized functional equations arising from distance measures
Kim, Gwang Hui,Lee, Young Whan International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.2
<P>In this paper, we obtain the superstability of the functional equation f (pr, qs) + g(ps, qr) = theta (pq, rs)h(p, q)k(r, s) for all p, q, r, s is an element of G, where G is an Abelian group, f, g, h, k are functionals on G(2), and theta is a cocycle on G(2). This functional equation is a generalized form of the functional equation f (pr, qs) + f (ps, qr) = f (p, q) f (r, s), which arises in the characterization of symmetrically compositive sum-form distance measures and the information measures, and also they can be represented as products of some multiplicative functions and the exponential functional equations. As corollaries, we obtain the superstability of the many functional equations (combination of three variables functions, for example: f (pr, qs) + g(ps, qr) = theta (pq, rs)h(p, q)g(r, s)). (C)2016 All rights reserved.</P>
A research on the some properties and distribution of zeros for Stirling polynomials
Kang, Jung Yoog,Ryoo, Cheon Seoung International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.4
<P>We find some identities of the Stirling polynomials and relations between these polynomials and other numbers and polynomials such as generalized Bernoulli numbers. We also display some properties and figures that are related to the distribution of fixed points in the Stirling polynomials from the Newton dynamical system containing iterated mapping. (C) 2016 All rights reserved.</P>
A regularity of split-biquaternionic-valued functions in Clifford analysis
Kim, Ji Eun,Shon, Kwang Ho International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.12
<P>We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. (C) 2016 all rights reserved.</P>
Bernoulli polynomials of the second kind and their identities arising from umbral calculus
Kim, Taekyun,Kim, Dae San,Dolgy , Dmitry V.,Seo, Jong-Jin International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.3
<P>In this paper, we study the Bernoulli polynomials of the second kind with umbral calculus viewpoint and derive various identities involving those polynomials by using umbral calculus. (C)2016 All rights reserved.</P>
Modified forward-backward splitting methods for accretive operators in Banach spaces
Pholasa, Nattawut,Cholamjiak, Prasit,Cho, Yeol Je International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.5
<P>In this paper, we propose the modified splitting method for accretive operators in Banach spaces and prove some strong convergence theorems of the proposed method under suitable conditions. Finally, we give some applications to the minimization problems. (C) 2016 All rights reserved.</P>
International Scientific Research Publications MY 2017 The journal of nonlinear science and applications Vol.10 No.8
<P>In this paper, we obtain a general symmetric identity involving the degenerate Euler-tangent mixed-type polynomials and sums of generalized falling factorials. We use this identity to describe some combinatorial relations between these polynomials and generalized factorial alternating sums. Finally, we observe an interesting phenomenon of 'scattering' of the zeros of degenerate Euler-tangent mixed-type polynomials. (C) 2017 All rights reserved.</P>
Caratheodory's approximate solution to stochastic differential delay equation
Cho, Yeol Je,Kim, Young-Ho International Scientific Research Publications MY 2017 The journal of nonlinear science and applications Vol.10 No.4
<P>In this paper, we show the difference between an approximate solution and an accurate solution for a stochastic differential delay equation, where the approximate solution, which is called by Caratheodory, is constructed by successive approximation. Furthermore, we study the p-th moment continuity of the approximate solution for this delay equation. (C) 2017 All rights reserved.</P>
Differential equations for Changhee polynomials and their applications
Kim, Taekyun,Dolgy, Dmitry V.,Kim, Dae San,Seo, Jong Jin International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.5
<P>Recently, the non-linear Changhee differential equations were introduced by Kim and Kim [T. Kim, D. S. Kim, Russ. J. Math. Phys., 23 (2016), 1-5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and properties of Changhee polynomials can also be derived from umbral calculus (see [D. S. Kim, T. Kim, J. J. Seo, Adv. Studies Theor. Phys., 7 (2013), 993-1003]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations. (C) 2016 All rights reserved.</P>
A class of differential inverse quasi-variational inequalities in finite dimensional spaces
Li, Wei,Xiao , Yi-Bin,Huang , Nan-Jing,Cho , Yeol Je International Scientific Research Publications MY 2017 The journal of nonlinear science and applications Vol.10 No.8
<P>In this paper, we introduce and study a class of differential inverse quasi-variational inequalities in finite dimensional Euclidean spaces, which are closely related to the differential variational inequalities. By using two important theorems on differential inclusions, we first prove some existence theorems for Caratheodory weak solutions of the differential inverse quasi-variational inequality considered. Then, with the Euler computation method, we construct an Euler time-dependent scheme for solving the differential inverse quasi-variational inequality and prove a convergence result on the Euler time-dependent scheme constructed. (C) 2017 All rights reserved.</P>
On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation
Bae, Jae-Hyeong,Park , Won-Gil International Scientific Research Publications MY 2015 The journal of nonlinear science and applications Vol.8 No.5
<P>In this paper, we investigate the Ulam stability of the functional equations 2f(x + y, z+w/2) = f(x,z) + f(x,w) + f(y,z) + f(y,w) and f (x + y, z + w) + f (x + y, z w) - 2f (x, z) + 2f (x,w) + 2f(y, z) + 2f(y,w) in paranormed spaces. (C) 2015 All rights reserved.</P>