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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The space of $(\psi,\gamma)$-additive mappings on semigroups


Authors: Valerii A. Faiziev, Themistocles M. Rassias and Prasanna K. Sahoo
Journal: Trans. Amer. Math. Soc. 354 (2002), 4455-4472
MSC (2000): Primary 20M15, 20M30, 39B82.
DOI: https://doi.org/10.1090/S0002-9947-02-03036-2
Published electronically: July 2, 2002
MathSciNet review: 1926883
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Abstract: In this paper, we introduce the concept of $(\psi,\gamma)$-pseudoadditive mappings from a semigroup into a Banach space, and we provide a generalized solution of Ulam's problem for approximately additive mappings.


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Additional Information

Valerii A. Faiziev
Affiliation: Tver State Agricultural Academy, Tver Sakharovo, Russia
Address at time of publication: Tereshkova Sq. 47/27–43, Tver 170037, Russia
Email: valeriy.fayziev@tversu.ru

Themistocles M. Rassias
Affiliation: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece
Email: trassias@math.ntua.gr

Prasanna K. Sahoo
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: sahoo@louisville.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03036-2
Keywords: Banach spaces, free group, metabelian group, metric group, semigroup, semidirect product of semigroups, stability, wreath product, $(\psi, \gamma)$--quasiadditive mapping, $(\psi, \gamma)$--pseudoadditive mapping.
Received by editor(s): November 20, 2000
Received by editor(s) in revised form: November 5, 2001
Published electronically: July 2, 2002
Dedicated: Dedicated to the memory of Maria
Article copyright: © Copyright 2002 American Mathematical Society