Abstract
In this research paper, we deal with the problem of determining the function χ:G→R, which is the solution to the maximum functional equation (MFE) max{χ(xy),χ(xy−1)}=χ(x)χ(y), when the domain is a discretely normed abelian group or any arbitrary group G. We also analyse the stability of the maximum functional equation max{χ(xy),χ(xy−1)}=χ(x)+χ(y) and its solutions for the function χ:G→R, where G be any group and also investigate the connection of the stability with commutators and free abelian group K that can be embedded into a group G.
Highlights
In this research paper, we deal with the problem of determining the function χ : G → R, which is the solution to the maximum functional equation (MFE) max{ χ( xy), χ( xy−1 ) } = χ( x )χ(y), when the domain is a discretely normed abelian group or any arbitrary group G
This paper is arranged, as follows: in Section 2, we prove the functional Equation (1) for any arbitrary group G without any characterisation of an additive function’s absolute value
We present the generalization of Theorem 2 by proposing a discretely normed abelian group G
Summary
Let G be a group and function χ : G → R satisfies the Kannappan condition max{ χ( xy), χ( xy−1 ) } = χ( x ) + χ(y) for all x, y ∈ G Let G be a group and function χ : G → R satisfies the Kannappan condition, and χ satisfies the Equation (3) if and only if χ( x ) + χ(y) = χ( xy) + χ( xy−1 ) − |χ( x ) − χ(y)|
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
