Stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces

Hyers Stability in Generalized Intuitionistic P-Pseudo Fuzzy 2-Normed Spaces

“…(4) Triangular inequality: Let g, h, j ∈ S such that d(g, h) ≤ η 1 and d(j, h) ≤ η 2 . Using (7), we have…”

“…It is enough to show that F satisfies (1). Putting p = q, v := r n v and u := r n u in (7), we obtain ρ µ,ν (D m f (r n u, r n v), ξ(r n u), 2p) ≥ Υ * τ ρ µ,ν (ϕ m (r n u, r n u), ψ m (r n u, r n u), p), (26)…”

“…for all u ∈ ∆. If f : ∆ → Θ is a mapping satisfying f (0) = 0 and the inequality (7), then there exists a unique m−mapping F : ∆ → Θ satisfying (3) such that…”

“…Similarly, by changing the type of functional equation in the above theorem from additive to quadratic, cubic, Jensen, etc., or replacing the functional equation with a differential or integral equation, the conditions of the stability theorem have been investigated and proven. We refer readers to [4][5][6][7][8][9][10][11][12][13] references for consideration of the stability of various functional equations in different spaces.…”

Hyers Stability and Multi-Fuzzy Banach Algebra

“…Mathematicians developed the results of the Hyers theorem. By changing the space, the norm, the control function, and functional equation, they could prove more interesting theorems [7][8][9][10][11][12][13][14]. For example, the Jenson functional equation or the integral and differential equations were used instead of the functional equation (in the theorem) and the validity of the theorem was proved.…”