# Search results

Acta Mathematica Hungarica > 2018 > 154 > 1 > 187-198

The Journal of Analysis > 2018 > 26 > 1 > 1-8

Aequationes mathematicae > 2017 > 91 > 4 > 647-661

Afrika Matematika > 2016 > 27 > 7-8 > 1377-1389

Arab Journal of Mathematical Sciences > 2015 > 21 > 1 > 67-83

Journal of Inequalities and Applications > 2015 > 2015 > 1 > 1-18

Mathematical Sciences > 2013 > 7 > 1 > 1-4

Mathematical and Computer Modelling > 2011 > 54 > 9-10 > 2403-2409

Applied Mathematics Letters > 2011 > 24 > 4 > 541-544

Journal of Inequalities and Applications > 2011 > 2011 > 1 > 1-8

*X*be a normed space and

*Y*be a Banach fuzzy space. Let

*D*= {(

*x*,

*y*) ∈

*X*×

*X*: ||

*x*|| + ||

*y*|| ≥

*d*} where

*d*> 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on

*D*and taking values in

*Y*. We consider also the Pexiderized Cauchy functional equation.

**2000 Mathematics Subject Classification:**39B22; 39B82; 46S10.

Journal of Mathematical Analysis and Applications > 2008 > 341 > 1 > 62-79

Fuzzy Sets and Systems > 2008 > 159 > 6 > 730-738

Bulletin des sciences mathematiques > 2008 > 132 > 2 > 87-96

Chinese Annals of Mathematics, Series B > 2007 > 28 > 3 > 353-362

Journal of Mathematical Analysis and Applications > 2007 > 325 > 1 > 237-248

Journal of Mathematical Analysis and Applications > 2006 > 324 > 2 > 1395-1406

Journal of Geometry > 2006 > 85 > 1-2 > 149-156

*X*,||·||) and (

*Y*,||·||) be normed linear spaces, dim

*X*, dim

*Y*≥ 2. We say that

*f*:

*X*→

*Y*

*preserves equilateral triangles*if for all triples of points

*x*,

*y*,

*z*∈

*X*with ||

*x*−

*y*|| = ||

*y*−

*z*|| = ||

*x*−

*z*|| we have $$||f (x) -f (y)||=||f (y)-f (z)||=||f (x)- f (z)||.$$ We prove that if

*X*and

*Y*are at least three-dimensional and

*f*:

*X*→

*Y*is surjective and preserves equilateral triangles, then...

Acta Mathematica Sinica, English Series > 2005 > 21 > 5 > 1159-1166

*f*

_{1}(2

*x*+

*y*) +

*f*

_{2}(2

*x*−

*y*) =

*f*

_{3}(

*x*+

*y*) +

*f*

_{4}(

*x*−

*y*) +

*f*

_{5}(

*x*) without assuming any regularity condition on the unknown functions

*f*

_{1},

*f*

_{2},

*f*

_{3},

*f*

_{4},

*f*

_{5}: ℝ → ℝ. The general solution of this equation is obtained by finding the general solution of the functional equations

*f*(2

*x*+

*y*) +

*f*(2

*x*−

*y*) =

*g*(

*x*+

*y*) +

*g*(

*x*−

*y*) +

*h*(

*x*) and...

Acta Mathematica Sinica, English Series > 2005 > 21 > 5 > 1159-1166

Results in Mathematics > 2004 > 46 > 3-4 > 381-388