Functional inequalities in non-Archimedean normed spaces
type: Item
instance of: scholarly article
title: Functional inequalities in non-Archimedean normed spaces
zbMATH Open document ID: 1315.39016
publication date: 2015-03-25T00:00:00Z
review text: By using classical methods, the author studies 4 functional inequalities, along with their Hyers-Ulam stability. Namely, \[ |f(x+ y)- f(x)- f(y)|\leq \Biggl| f\Biggl({x+y\over 2}\Biggr)- {1\over 2} f(x)-{1\over 2} f(y)\Biggr|, \] and \[ |f(x+ y)+ f(x- y)- 2f(x)- 2f(y)|\leq\Biggl| f\Biggl({x+ y\over 2}\Biggr)+ f\Biggl({x-y\over 2}\Biggr)- {1\over 2} f(x)- {1\over 2} f(y)\Biggr| \] in Banach spaces, as well as \[ \Biggl| f\Biggl({x+y\over 2}\Biggr)- {1\over 2} f(x)-{1\over 2} f(y)\Biggr|\leq |f(x+y)- f(x)- f(y)| \] and \[ \Biggl| f\Biggl({x+y\over 2}\Biggr)+ f\Biggl({x-y\over 2}\Biggr)-{1\over 2} f(x)-{1\over 2} f(y)\Biggr|\leq |f(x+ y)+ f(x- y)- 2f(x)- 2f(y)| \] in non-Archimedean Banach spaces.
reviewed by: József Sándor
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 6419643
zbMATH Keywords: functional inequalities
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: Jordan-von Neumann functional equation
zbMATH Keywords: non-Archimedean normed space
zbMATH Keywords: Banach space
author: Choonkil Park
MaRDI profile type: Publication
full work available at URL: s10114-015-4278-5
OpenAlex ID: W2117500328
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DOI: 10.1007/S10114-015-4278-5
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 6419643