Stability of Bi-Additive Mappings and Bi-Jensen Mappings

Symmetry is repetitive self-similarity. We proved the stability problem by replicating the well-known Cauchy equation and the well-known Jensen equation into two variables. In this paper, we proved the Hyers-Ulam stability of the bi-additive functional equation f(x+y,z+w)=f(x,z)+f(y,w) and the bi-Jensen functional equation 4fx+y2,z+w2=f(x,z)+f(x,w)+f(y,z)+f(y,w).

Stability of a ramanujan type additive functional equation

In this paper, the authors achieve the generalized Ulam - Hyers stability of a Ramanujan Type Additive Functional Equation in Paranormed Spaces and Modular spaces via classical Hyers Method.

Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.

STABILITY ANALYSIS IN BANACH SPACES FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION

In this paper, we present the Hyers-Ulam stability of generalized additive functional equation in Banach spaces and stability results have been obtained by a classical direct method by various general control functions.

Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.