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

Tianzhou Xu (), Yali Ding () and John Michael Rassias ()
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Tianzhou Xu: Beijing Institute of Technology, School of Mathematics and Statistics
Yali Ding: Shaanxi University of Science and Technology, School of Arts and Sciences
John Michael Rassias: Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 309-323 from Springer

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

Keywords: Stability; Additive-quadratic-quartic functional equation; Fixed point theorem; Primary 39B82; Secondary 39B52 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/978-3-030-28950-8_18

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