### Abstract

In this paper, we introduce and solve the following additive (ρ_{1}, ρ_{2})-functional in-equalities [Formula presented] where ρ_{1} and ρ_{2} are fixed complex numbers with |ρ_{1}| ·|ρ_{2}| ˃ 1, and [formula presented] where ρ_{1} and ρ_{2} are fixed complex numbers with |ρ_{1}| ˃ 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ_{1}, ρ_{2})-functional inequalities (0.1) and (0.2) in complex Banach spaces.

Original language | English |
---|---|

Pages (from-to) | 367-379 |

Number of pages | 13 |

Journal | Journal of Computational Analysis and Applications |

Volume | 27 |

Issue number | 2 |

State | Published - 2019 Aug 1 |

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### Keywords

- Additive (ρ,ρ)-functional inequality
- Banach space
- Direct method
- Fixed point method
- Hyers-Ulam stability

### Cite this

_{1}, ρ

_{2})-functional inequalities in complex Banach spaces.

*Journal of Computational Analysis and Applications*,

*27*(2), 367-379.

}

_{1}, ρ

_{2})-functional inequalities in complex Banach spaces',

*Journal of Computational Analysis and Applications*, vol. 27, no. 2, pp. 367-379.

**Additive (ρ _{1}, ρ_{2})-functional inequalities in complex Banach spaces.** / Park, Choonkil; Shin, Dong Yun; Anastassiou, George A.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Additive (ρ1, ρ2)-functional inequalities in complex Banach spaces

AU - Park, Choonkil

AU - Shin, Dong Yun

AU - Anastassiou, George A.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - In this paper, we introduce and solve the following additive (ρ1, ρ2)-functional in-equalities [Formula presented] where ρ1 and ρ2 are fixed complex numbers with |ρ1| ·|ρ2| ˃ 1, and [formula presented] where ρ1 and ρ2 are fixed complex numbers with |ρ1| ˃ 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ2)-functional inequalities (0.1) and (0.2) in complex Banach spaces.

AB - In this paper, we introduce and solve the following additive (ρ1, ρ2)-functional in-equalities [Formula presented] where ρ1 and ρ2 are fixed complex numbers with |ρ1| ·|ρ2| ˃ 1, and [formula presented] where ρ1 and ρ2 are fixed complex numbers with |ρ1| ˃ 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ2)-functional inequalities (0.1) and (0.2) in complex Banach spaces.

KW - Additive (ρ,ρ)-functional inequality

KW - Banach space

KW - Direct method

KW - Fixed point method

KW - Hyers-Ulam stability

UR - http://www.scopus.com/inward/record.url?scp=85045452878&partnerID=8YFLogxK

M3 - Article

VL - 27

SP - 367

EP - 379

JO - Journal of Computational Analysis and Applications

JF - Journal of Computational Analysis and Applications

SN - 1521-1398

IS - 2

ER -

_{1}, ρ

_{2})-functional inequalities in complex Banach spaces. Journal of Computational Analysis and Applications. 2019 Aug 1;27(2):367-379.