On Direct Fuzzy Stability of General Quartic Functional Equation

Shalini Tomar

doi:10.9734/arjom/2023/v19i9696

On Direct Fuzzy Stability of General Quartic Functional Equation

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Published: 2023-06-27

DOI: 10.9734/arjom/2023/v19i9696

Page: 25-31

Issue: 2023 - Volume 19 [Issue 9]

Shalini Tomar *

Kanya Mahavidyalaya, Kharkhoda, Sonepat, Haryana, India.

*Author to whom correspondence should be addressed.

Abstract

The goal of this paper is to investigate the Generalized Hyers - Ulam - Rassias (HUR) stability of general
quartic functional equation (GQFE)

f_q(kr₁ + (k -1)r2) + f_q(kr₁ - (k -1)r₂) = 2k⁴f_q(r₁) + 2(k -1)⁴f_q(r₂)
+6k²(k -1)²[f_q(r₁ + r₂) + f_q(r₁ - r₂)] - 12k²(k - 1)²[f_q(r₁) + f_q(r₂)]

in fuzzy normed spaces (F.N. spaces). The stability of the equation is proved by using direct method. The stability in sense of Hyers - Ulam and Ulam- Gavruta - Rassias is also studied.

Keywords: Generalised Hyers - Ulam - Rassias (HUR) stability;, fuzzy normed space, general quartic functional equation

How to Cite

Tomar, Shalini. 2023. “On Direct Fuzzy Stability of General Quartic Functional Equation”. Asian Research Journal of Mathematics 19 (9):25-31. https://doi.org/10.9734/arjom/2023/v19i9696.

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