Additive-Quadratic Functional Inequalities

Choonkil Park () and Themistocles M. Rassias ()
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Choonkil Park: Hanyang University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Computational Mathematics and Variational Analysis, 2020, pp 315-341 from Springer

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

Date: 2020
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DOI: 10.1007/978-3-030-44625-3_18

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