QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

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

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1501-1510.doi: 10.1016/S0252-9602(15)30071-0

QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

Choonkil PARK

Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea

收稿日期:2014-04-30 出版日期:2015-11-01 发布日期:2015-11-01
作者简介:Choonkil PARK, E-mail: baak@hanyang.ac.kr
基金资助:
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).

QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

Choonkil PARK

Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea

Received:2014-04-30 Online:2015-11-01 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).

摘要/Abstract

摘要：

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.

关键词: Hyers-Ulam stability, quadratic ρ-functional equation, quadratic ρ-functional inequality, complex Banach space

Abstract:

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

中图分类号:

39B62

Choonkil PARK. QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES[J]. 数学物理学报(英文版), 2015, 35(6): 1501-1510.

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

参考文献

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QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

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