Additive ρ-Functional Inequalities and Their Applications

Jung Rye Lee (), Choonkil Park (), Themistocles M. Rassias () and Xiaohong Zhang ()
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Jung Rye Lee: Daejin University
Choonkil Park: Hanyang University
Themistocles M. Rassias: National Technical University of Athens
Xiaohong Zhang: Shanghai Maritime University

A chapter in Mathematical Analysis and Applications, 2019, pp 391-410 from Springer

Abstract: Abstract In this paper, we solve the additive ρ-functional inequalities 1 ∥ f ( x + y + z ) − f ( x ) − f ( y ) − f ( z ) ∥ ≤ ρ 2 f x + y 2 + z − f ( x ) − f ( y ) − 2 f ( z ) , $$\displaystyle \begin{aligned} \begin{array}{rcl}{} &\displaystyle &\displaystyle \|f(x+y+z)- f(x)-f(y)- f(z)\| \\ &\displaystyle &\displaystyle \qquad \qquad \le \left\|\rho\left(2 f\left(\frac{x+y}{2}+z \right)-f(x) - f(y)- 2f(z) \right)\right\|, \end{array} \end{aligned} $$ where ρ is a fixed complex number with |ρ|

Date: 2019
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DOI: 10.1007/978-3-030-31339-5_14

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