Additive-Quadratic ρ-Functional Equations in β-Homogeneous Normed Spaces

Jung Rye Lee (), Choonkil Park (), Themistocles M. Rassias () and Sungsik Yun ()
Additional contact information
Jung Rye Lee: Daejin University, Department of Mathematics
Choonkil Park: Hanyang University, Department of Mathematics
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics
Sungsik Yun: Hanshin University, Department of Financial Mathematics

A chapter in Approximation Theory and Analytic Inequalities, 2021, pp 309-323 from Springer

Abstract: Abstract Let M 1 f ( x , y ) : = 3 4 f ( x + y ) − 1 4 f ( − x − y ) + 1 4 f ( x − y ) + 1 4 f ( y − x ) − f ( x ) − f ( y ) $$M_1f(x,y) : = \frac {3}{4} f(x+y) - \frac {1}{4}f(-x-y) + \frac {1}{4} f(x-y) + \frac {1}{4} f(y-x) - f(x) - f(y)$$ and M 2 f ( x , y ) : = 2 f x + y 2 + f x − y 2 + f y − x 2 − f ( x ) − f ( y ) . $$M_2 f(x,y): = 2 f\left ( \frac {x+y}{2} \right ) + f\left ( \frac {x-y}{2}\right ) + f\left ( \frac {y-x}{2}\right ) - f(x) - f(y).$$ We solve the additive-quadratic ρ-functional inequalities 1 ∥ M 1 f ( x , y ) ∥ ≤ ∥ ρ M 2 f ( x , y ) ∥ , $$\displaystyle \begin{array}{@{}rcl@{}} {} {}\| M_1 f(x,y)\| \le \|\rho M_2f(x,y)\|, \end{array} $$ where ρ is a fixed complex number with | ρ |

Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-60622-0_16

Ordering information: This item can be ordered from
http://www.springer.com/9783030606220

DOI: 10.1007/978-3-030-60622-0_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().