Explicit Solutions of the Invariance Equation for Means
نویسندگان
چکیده
منابع مشابه
On the Invariance Equation for Heinz Means
We solve the so-called invariance equation in the class of Heinz means, that is, we give necessary and sufficient conditions for the constants 0 p,q,r 1 such that the identity Hp(Hq(x,y),Hr(x,y)) = Hp(x,y) (x,y ∈ R+) holds true where the Heinz mean Hp is defined for 0 p 1 as Hp(x,y) = xpy1−p + x1−pyp 2 . The Taylor expansion of the Heinz mean is used. Mathematics subject classification (2010): ...
متن کاملExact and explicit solutions for the discrete Burgers equation by means of the Exp-function method
In recent years, various direct methods were proposed to find exact solutions not only for nonlinear partial differential equations but also for nonlinear differential-difference equations (NDDEs). In this paper, the Exp-function method was extended to the discrete Burgers equation for searching traveling waves in closed forms. It was shown that the equation supported discrete solitary wave sol...
متن کاملAnalytical solutions for the fractional Fisher's equation
In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...
متن کاملExplicit multiple singular periodic solutions and singular soliton solutions to KdV equation
Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...
متن کاملSolutions of diffusion equation for point defects
An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solutio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2016
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-015-0525-4