Tbilisi Mathematical Journal

A fixed point approach to Ulam-Hyers stability of duodecic functional equation in quasi-$β$-normed spaces

J. M. Rassias, K. Ravi, and B. V. Senthil Kumar

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Abstract

In this study, we achieve the general solution and investigate Ulam-Hyers stabilities involving a general control function, sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms of the duodecic functional equation in quasi-$β$-normed spaces via fixed point method. We also illustrate a counter-example for non-stability of the duodecic functional equation in singular case.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 4 (2017), 83-101.

Dates
Received: 24 February 2017
Accepted: 25 September 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276060

Digital Object Identifier
doi:10.1515/tmj-2017-0048

Mathematical Reviews number (MathSciNet)
MR3719329

Zentralblatt MATH identifier
1377.39044

Subjects
Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 39B72: Systems of functional equations and inequalities

Keywords
quasi-$β$-normed spaces duodecic mapping $(β,p)$-Banach spaces generalized Ulam-Hyers stability

Citation

Rassias, J. M.; Ravi, K.; Kumar, B. V. Senthil. A fixed point approach to Ulam-Hyers stability of duodecic functional equation in quasi-$β$-normed spaces. Tbilisi Math. J. 10 (2017), no. 4, 83--101. doi:10.1515/tmj-2017-0048. https://projecteuclid.org/euclid.tbilisi/1524276060


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