Functional inequalities in non-Archimedean normed spaces
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.
scientific article; zbMATH DE number 6419643
scientific article