Journal of Guangdong University of Technology ›› 2022, Vol. 39 ›› Issue (02): 72-75.doi: 10.12052/gdutxb.210017

Previous Articles     Next Articles

Solutions of Some Generalized Pexider Equations

Xiao Zhi-tao   

  1. Guangzhou Huali College, Guangzhou 511325, China
  • Received:2021-01-28 Online:2022-03-10 Published:2022-04-02

Abstract: The general forms of pexider additive function equation, pexider exponential function equation, pexider logarithmic function equation and pexider power function equation are discussed, and the general solutions of these equations are given.

Key words: pexider equation, additive function equation, exponential function equation, logarithmic function equation, power function equation

CLC Number: 

  • O175
[1] PEXIDER J V. Notizuber funktionltheoreme[J]. Monatsh Math Phy, 1903, 14: 293-301.
[2] RADO F, BAKER J A. Pexider’s equation and aggregation of allocations[J]. Aequationes Mathematicae, 1987, 32: 227-239.
[3] NG C T. A Pexider-Jensen equation on groups [J]. Aequationes Math, 2005, 70(1/2): 131-153.
[4] ACZEL J, SKOF F. Local Pexider and cauchy equations [J]. Aequationes Math, 2007, 73(3): 311-320.
[5] BARBARA S. Pexider equation on a restricted domain [J]. Demonstratio Math, 2010, XLIII(1): 81-88.
[6] ACZEL J. Extension of a generalized Pexider equation[J]. Proc Am Math Soc, 2005, A133: 3227-3233.
[7] BAJER M. A generalized Pexider equation [J]. Acta Mathematica Hungarica, 1997, 75(1/2): 43-54.
[8] YUN S, PARK S. The stability of quadratic $ \alpha $ -functional equations [J]. Journal of Mathematical Sciences and Applications, 2016, 9(6): 3980-3991.
[9] ZI Y, LU G, YUAN F J, et al. The stability of additive $ \left( {\alpha, \beta } \right) $-functional equations[J]. Journal of Applied Analysis and Computation, 2019(6): 2295-2307.
[10] MURSALEEN M, MOHIUDDINE S A, KHURSHEED J, et al. On the stability of fuzzy set-valued functional equations[J]. Congent Mathematics, 2017(4): 1-12.
[11] YANG X, SHEN G, LIU G. On the stability of the functional equations in matrix normed spaces [J]. Journal of Mathematical Research with Applications, 2016, 36(3): 328-340.
[12] SONG J S, LI Y H. Hyers-Ulam-Rassias stability of a quadratic-additive type function equation in fuzzy space [J]. International Electronic Journal of Pure and Applied Mathematics, 2015, 9(3): 121-136.
[13] 徐林, 宋常修. 一类三阶时滞微分方程的稳定性和有界性[J]. 广东工业大学学报, 2015, 32(1): 128-132.
XU L, SONG C X. Stability and boundedness of a class of third-order delay differential equations [J]. Journal of Guangdong University of Technology, 2015, 32(1): 128-132.
[14] 黄慧敏, 郭承军. 一类脉冲随机微分方程解的稳定性[J]. 广东工业大学学报, 2020, 37(6): 56-62.
HUANG H M, GUO C J. Stability of solutions for a class of impulsive stochastic differential equations[J]. Journal of Guangdong University of Technology, 2020, 37(6): 56-62.
[15] ACZEL J. Lectures on Function Equations and Their Applications[M]. New York: Academic Press, 1966.
[16] GUIASU S. Information Theory with Applications[M]. New York: McGraw-Hill, 1977.
[1] Zhou Yun, Wei Xue-mei. A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary [J]. Journal of Guangdong University of Technology, 2021, 38(02): 60-65.
[2] Huang Hui-min, Guo Cheng-jun. Stability of Solutions for a Class of Impulsive Stochastic Differential Equations [J]. Journal of Guangdong University of Technology, 2020, 37(06): 56-62.
[3] Chen Rong-ning, Wei Xue-mei. Weak Well-posedness for the Generalized Camassa-Holm Equation [J]. Journal of Guangdong University of Technology, 2020, 37(02): 80-86.
[4] Liang Xiao-zhen, Wei Xue-mei. Existence of the Solution to the Metabolic Model of Colon Cancer Cells [J]. Journal of Guangdong University of Technology, 2019, 36(05): 38-42.
[5] Zhu Ya-jie, Zhu Hong-bo. An Asymptotically Linear Schrödinger Equation on RN [J]. Journal of Guangdong University of Technology, 2019, 36(02): 78-85.
[6] Chen Mei-gui, Wei Xue-mei. Existence and Uniqueness of Global Solution for a Model of Retinal Oxygen Distribution and the Role of Neuroglobin [J]. Journal of Guangdong University of Technology, 2018, 35(05): 45-50.
[7] Jin Ying-hua, Xiang Si-yuan. Mean-shift Test Based on φ-divergence Measure for Log-linear Model [J]. Journal of Guangdong University of Technology, 2018, 35(04): 32-36.
[8] Lu Yu. Existence of Solutions for a Class of FourthOrder BVP [J]. Journal of Guangdong University of Technology, 2014, 31(2): 69-73.
[9] Tang Hao-yi, Peng Hong-yun. Global Weak Solutions and Asymptotics of a 3D Chemotaxis System [J]. Journal of Guangdong University of Technology, 2022, 39(01): 93-98.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!