Stability of Bi-additive s-Functional Inequalities and Quasi-multipliers

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 325-337 from Springer

Abstract: Abstract Park et al. (Rocky Mt J Math 49, 593–607 (2019)) solved the following bi-additive s-functional inequalities: 1 ∥ f ( x + y , z − w ) + f ( x − y , z + w ) − 2 f ( x , z ) + 2 f ( y , w ) ∥ ≤ s 2 f x + y 2 , z − w + 2 f x − y 2 , z + w − 2 f ( x , z ) + 2 f ( y , w ) , $$\displaystyle \begin{array}{@{}rcl@{}} {} && \| f(x{+}y, z{-}w) {+} f(x{-}y, z{+}w) {-}2f(x,z){+}2 f(y, w)\| \\ && \quad \le \left \|s \left (2f\left (\frac {x{+}y}{2}, z{-}w\right ) {+} 2f\left (\frac {x{-}y}{2}, z{+}w\right ) {-} 2f(x,z ){+} 2 f(y, w)\right )\right \| , \end{array} $$ 2 2 f x + y 2 , z − w + 2 f x − y 2 , z + w − 2 f ( x , z ) + 2 f ( y , w ) ≤ s f ( x + y , z − w ) + f ( x − y , z + w ) − 2 f ( x , z ) + 2 f ( y , w ) , $$\displaystyle \begin{array}{@{}rcl@{}} {} && \left \|2f\left (\frac {x+y}{2}, z-w\right ) +2 f\left (\frac {x-y}{2}, z+w\right ) -2 f(x,z )+2 f(y, w)\right \| \\ && \quad \le \left \|s \left ( f(x+y, z-w) + f(x-y, z+w) -2f(x,z) +2 f(y, w) \right )\right \| , \end{array} $$ where s is a fixed nonzero complex number with |s|

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_17

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

DOI: 10.1007/978-3-030-60622-0_17

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 ().