Approximate Solutions of an Additive-Quadratic-Quartic (AQQ) Functional Equation

  • Tianzhou XuEmail author
  • Yali Ding
  • John Michael Rassias


In this paper, the authors prove some stability and hyperstability results for an (AQQ): additive-quadratic-quartic functional equation of the form
$$\displaystyle \begin{aligned} \begin{array}{rcl} &\displaystyle &\displaystyle f(x+y+z)+ f(x+y-z)+ f(x-y+z)+f(x-y-z) \\ &\displaystyle &\displaystyle \quad =2[f(x+y)+ f(x-y)+f(y+z)+f(y-z)+ f(x+z)+ f(x-z)] \\ &\displaystyle &\displaystyle \qquad -4f(x) - 4f(y) -2[f(z) + f(-z)] \end{array} \end{aligned} $$
by using fixed point theory.


Stability Additive-quadratic-quartic functional equation Fixed point theorem 

Mathematics Subject Classification

Primary 39B82; Secondary 39B52 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingPeople’s Republic of China
  2. 2.School of Arts and SciencesShaanxi University of Science and TechnologyXianPeople’s Republic of China
  3. 3.National and Kapodistrian University of AthensPedagogical Department E. E., Section of Mathematics and InformaticsAthensGreece

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