Acta mathematica scientia, Series B >
QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES
Received date: 2014-04-30
Online published: 2015-11-01
Supported by
This work was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF- 2012R1A1A2004299).
In this paper, we solve the quadratic ρ-functional inequalities
||f(x + y) + f(x y) 2f(x)2f(y)||≤||ρ(2f((x+y)/2)+2f((x-y)/2)f(x) f(y)||, (0.1)
where ρ is a fixed complex number with |ρ|< 1, and
||2f((x+y)/2)+2f((x-y)/2)f(x) f(y)||≤||ρf(x + y) + f(x y) 2f(x)2f(y)||, (0.2)
where ρ is a fixed complex number with |ρ|< 1/2 .Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic -functional equations associated with the quadratic ρ-functional inequalities (0.1)and (0.2) in complex Banach spaces.
Choonkil PARK . QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2015 , 35(6) : 1501 -1510 . DOI: 10.1016/S0252-9602(15)30071-0
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