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

Choonkil Park, Dong Yun Shin, George A. Anastassiou

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

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.

Original language English 367-379 13 Journal of Computational Analysis and Applications 27 2 Published - 2019 Aug 1

### Fingerprint

Functional Inequalities
Banach spaces
Complex number
Banach space
Hyers-Ulam Stability
Fixed Point Method
Direct Method
Equality

### Keywords

• Banach space
• Direct method
• Fixed point method
• Hyers-Ulam stability

### Cite this

Park, Choonkil ; Shin, Dong Yun ; Anastassiou, George A. / Additive (ρ1, ρ2)-functional inequalities in complex Banach spaces. In: Journal of Computational Analysis and Applications. 2019 ; Vol. 27, No. 2. pp. 367-379.
title = "Additive (ρ1, ρ2)-functional inequalities in complex Banach spaces",
abstract = "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.",
keywords = "Additive (ρ,ρ)-functional inequality, Banach space, Direct method, Fixed point method, Hyers-Ulam stability",
author = "Choonkil Park and Shin, {Dong Yun} and Anastassiou, {George A.}",
year = "2019",
month = "8",
day = "1",
language = "English",
volume = "27",
pages = "367--379",
journal = "Journal of Computational Analysis and Applications",
issn = "1521-1398",
number = "2",

}

Additive (ρ1, ρ2)-functional inequalities in complex Banach spaces. / Park, Choonkil; Shin, Dong Yun; Anastassiou, George A.

In: Journal of Computational Analysis and Applications, Vol. 27, No. 2, 01.08.2019, p. 367-379.

Research output: Contribution to journalArticleResearchpeer-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 - 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 -