QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

doi:10.1016/S0252-9602(15)30071-0

Abstract

Abstract:

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.

Key words: Hyers-Ulam stability, quadratic ρ-functional equation, quadratic ρ-functional inequality, complex Banach space

CLC Number:

39B62

Choonkil PARK. QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2015, 35(6): 1501-1510.

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