Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach spaces

Volume 32, Issue 4, pp 295--317 http://dx.doi.org/10.22436/jmcs.032.04.02

Publication Date: October 26, 2023 Submission Date: July 12, 2023 Revision Date: July 24, 2023 Accteptance Date: August 25, 2023

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Authors

S. Murugesan - Department of Mathematics, Sree Abiraami Arts \(\&\) Science College for Women, Gudiyattam, Vellore Dt. - 635 803, Tamil Nadu, India. P. S. Arumugam - Department of Mathematics, Rajalakshmi Engineering College (Autonomous), Thandalam, Chennai - 602105, Tamil Nadu, India. G. Gandhi - Department of Mathematics, R.M.D Engineering College, Kavaraipettai, Thiruvallur Dt. - 601 206, Tamil Nadu, India. V. Mani - Department of Mathematics, School of Advanced Science, Vellore Institute of Technology, Vellore - 632 014, Tamil Nadu, India. S. Srinivasan - Department of Mathematics, Panimalar Engineering College, Chennai, Tamil Nadu, India.

Abstract

In this paper, our main objective is to study the Hyers-Ulam-Gavruta stability of a Jensen's type quadratic-quadratic mapping in 2-Banach Spaces, that is, we prove the Hyers-Ulam-Gavruta stability of the Jensen's type functional equation \[ g \left( \dfrac{x+y}{2} + z \right) + g \left( \dfrac{x+y}{2} - z \right) + g \left( \dfrac{x-y}{2} + z \right) + g \left( \dfrac{x-y}{2} - z \right) = g(x) + g(y) + 4 g(z) ,\] in 2-Banach spaces by Hyers direct method.

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Keywords

• Hyers-Ulam-Gavruta stability
• Jensen's type mapping
• quadratic function
• invex set
• direct method

MSC

•  39B82
•  39B52
•  46B99
•  39B72
•  39B22
•  34K20

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