We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives ofΔ2-conditions.

In this paper, we prove the generalized UHR stability of a quartic functional equations f(2x + y) + f(2x − y) = 4f(x + y) + 4f(x − y) + 24f(x) − 6f(y) via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces by the modular which is l.s

By using the fixed point technique, we prove the stability of sixtic functional equations. Our results are studied and proved in the framework of fuzzy modular spaces (briefly, FM-spaces). The lower semi continuous (briefly, l.s.c.) and β-homogeneous are necessary conditions for this work.

We established some theorems under the aim of deriving variants of the Banach contraction principle, using the classes of inner contractions and outer contractions, on the structure of fuzzy modular spaces.