Abstract
In this research paper, the authors present a new mixed Euler-Lagrange σ -cubic-quartic functional equation. For this introduced mixed type functional equation, the authors obtain general solution and investigate the various stabilities related to the Ulam problem in Felbin’s type of fuzzy normed linear space (f-NLS) with suitable counterexamples. This approach leads us to approximate the Euler-Lagrange σ -cubic-quartic functional equation with better estimation.
Highlights
One of the famous questions concerning the stability of homomorphisms was raised by Ulam [1] in 1940
We show the set of all fuzzy real numbers by ΛðRÞ
We show the set of all nonnegative fuzzy real numbers by Λ∗ðRÞ
Summary
One of the famous questions concerning the stability of homomorphisms was raised by Ulam [1] in 1940. Ξ is said to be a nonnegative fuzzy real number when ξ ∈ ΛðRÞ and ξðτÞ = 0 for τ < 0. The stability problems of several functional equations (FEs) have been extensively investigated by a number of authors [4, 9,10,11,12,13,14,15,16,17,18,19,20] in Felbin type f-NLS. Á 1 fπð2tÞ πð2sÞg, ð2Þ where σ ∈ R − f0,±1g For this mixed type FE, authors obtain the general solution and investigate the various stabilities related to Ulam problem [1] in Felbin’s type f-NLS with suitable counterexamples
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