两类广义对数函数方程和Pexider推广(英文)

函数方程在数学、空气动力学和动态经济学等领域都被涉及,因此函数方程的研究对科学技术的发展和国民经济建设都有重要的作用.众所周知的对数函数方程在实践中具有广泛的应用,近年来,它引起了研究者的关注.在这篇文章中,我们证明了两类广义对数函数方程与古典对数函数方程等效.对其中一类广义对数函数方程,我们讨论了它的Pexider方程,并给出了它的通解.对另一类广义对数函数方程,我们也讨论了它的Pexider方程,并给出了它的二次可微解,从而推广了文献(K.J.Heuvers,P.Kannappan.Aequationes Math,2005,70:117-121.)和(K.J.Heuvers.Aequationes Math,1999,58:260-264.)的相关结果.

Two Classes of Generalized Logarithmic Functional Equations and Pexider Generalizations

Functional equations are involved in the fields of mathematics,aerodynamics,economic dynamics,etc,so,the study of functional equations is very important for the development of sciences,technologies and national economic construction.The logarithmic functional equations are widely used in practice,and attract the attention of researchers in recent years.In this paper we prove that two classes of generalized logarithmic functional equations are equivalent to the classical logarithmic functional equations.For one class of generalized logarithmic functional equations,we discuss their Pexider equations and get their general solutions.For the other one,we consider the second order differentiable solutions of their Pexider equations.The related results in the papers(K.J.Heuvers,P.Kannappan.Aequationes Math,2005,70: 117-121.) and(K.J.Heuvers.Aequationes Math,1999,58: 260-264.) are generalized.