Solutions and Stability of Some Functional Equations on Semigroups

Keltouma Belfakih, Elhoucien Elqorachi and Themistocles M. Rassias ()
Additional contact information
Keltouma Belfakih: University Ibn Zohr, Department of Mathematics, Faculty of Sciences
Elhoucien Elqorachi: University Ibn Zohr, Department of Mathematics, Faculty of Sciences
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics

Chapter Chapter 9 in Ulam Type Stability, 2019, pp 167-198 from Springer

Abstract: Abstract In this paper we investigate the solutions and the Hyers-Ulam stability of the μ-Jensen functional equation f ( x y ) + μ ( y ) f ( x σ ( y ) ) = 2 f ( x ) , x , y ∈ S , $$\displaystyle f(xy)+\mu (y)f(x\sigma (y))=2f(x),\;x,y \in S, $$ a variant of the μ-Jensen functional equation f ( x y ) + μ ( y ) f ( σ ( y ) x ) = 2 f ( x ) , x , y ∈ S , $$\displaystyle f(xy)+\mu (y)f(\sigma (y)x)=2f(x),\;x,y \in S, $$ and the μ-quadratic functional equation f ( x y ) + μ ( y ) f ( x σ ( y ) ) = 2 f ( x ) + 2 f ( y ) , x , y ∈ S , $$\displaystyle f(xy)+\mu (y)f(x\sigma (y))=2f(x)+2f(y),\;x,y \in S, $$ where S is a semigroup, σ is a morphism of S and μ: S → ℂ $$S\longrightarrow \mathbb {C}$$ is a multiplicative function such that μ(xσ(x)) = 1 for all x ∈ S.

Keywords: Functional equation; Hyers-Ulam stability; μ-Jensen functional equation; μ-Quadratic functional equation; Primary 49B82; Secondary 39C52, 39C62 (search for similar items in EconPapers)
Date: 2019
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:978-3-030-28972-0_9

Ordering information: This item can be ordered from
http://www.springer.com/9783030289720

DOI: 10.1007/978-3-030-28972-0_9

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 ().