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    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/117/01/0031-0048

    • Keywords

       

      Additive mapping; Banach spaces; Jensen equation; Jensen function; metabelian group; metric group; pseudoadditive mapping; pseudo-Jensen function; pseudocharacter; quasiadditive map; quasicharacter; quasi-Jensen function; semigroup; direct product of groups; <

    • Abstract

       

      In this paper we establish the stability of Jensen’s functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and $T(2,K)$, where 𝐾 is an arbitrary commutative field with characteristic different from two. We also prove that any group 𝐴 can be embedded into some group 𝐺 such that the Jensen functional equation is stable on 𝐺.

    • Author Affiliations

       

      Valeriĭ A Faĭziev1 Prasanna K Sahoo2

      1. Tver State Agricultural Academy, Tver Sakharovo, Russia
      2. Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

    • Dates

       
      Published
      February 2007
      Manuscript received
      17 March 2005

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