Abstract
This paper presents the generalized Ulam-Hyers stability of the following quadratic functional equationF((x+y)/2 – z) + f(y+z)/2 – x) + f((z+x)/2 – y) = 3/4(f(z−x) + f(z−y) + f(x−y))in Felbin’s type fuzzy normed linear spaces (f-NLS) using direct and fixed point methods.
Highlights
This paper presents the generalized Ulam-Hyers stability of the following quadratic functional equation x +y y +z z +x f 2 − z + f 2 − x + f 2 − y = 4 (f (z − x) + f (z − y ) + f (x − y ))
Rassias [28] provided a lot of influence for the development of stability theory of a large variety of functional equations
This paper presents the generalized Ulam-Hyers stability of the following quadratic functional equation x +y y +z z +x f 2 −z +f 2 −x +f 2 −y
Summary
In 1978, Th.M.Rassias [28] proved a further generalzation of Hyers’ Theorem by introducing the concept of the unbounded Cauchy difference for the sum of powers of two p−norms. During the last three decades the stability theorem of Th.M. Rassias [28] provided a lot of influence for the development of stability theory of a large variety of functional equations. Rassias [28] provided a lot of influence for the development of stability theory of a large variety of functional equations This new concept is known today with the term Hyers-Ulam-Rassias. Quadratic functional equation; generalized Ulam-Hyers stability; Felbin’s fuzzy normed linear space. This paper presents the generalized Ulam-Hyers stability of the following quadratic functional equation x +y y +z z +x f 2 −z +f 2 −x +f 2 −y. In Felbin’s fuzzy normed linear spaces (f-NLS) using direct and fixed point methods
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