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Using the direct approach, the authors find the Ulam stability of the septic functional equation and octic functional equation in Felbin’s type non-Archimedean fuzzy normed space. [ABSTRACT FROM AUTHOR]

For any rational numbers k, l with kl(l −1) ̸= 0, we prove the generalized Hyers–Ulam stability of the Euler-Lagrange quadratic functional equation f(kx + ly) + f(kx − ly) + 2(l − 1)[k²f(x) − lf(y)] = l[f(kx + y) + f(kx − y)] using both the direct method and fixed point method in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new generalized multifarious radical reciprocal functional equation by generalizing the equation employed by Narasimman et al. in [5] and combining three classical Pythagorean means arithmetic, geometric and harmonic. Also, we illustrate the geometrical interpretation. Mainly, we find its general solution and stabilities related to Ulam problem in modular spaces by using fixed point approach. [ABSTRACT FROM AUTHOR]

In this paper, we find solutions and investigate the superstability bounded by function for the sine functional equation (S) from the approximate inequality of the Pexider type functional equation: f (x+y/2)²-g(x-y/2)2 = h(x)k(y). Furthermore, the results are extended to Banach algebras. As a consequence, we obtain the superstability for the exponential functional equations, the hyperbolic functional equations, and the jointed Pexider Lobacevski equation. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the stability problems for the following quadratic functional equation f(x+y+z)+f(x+y-z)+f(x-y+z)+f(-x+y+z) = 4f(x)+4f(y)+4f(z) on an unbounded restricted domain. As a consequence, we can apply the obtained results to obtain some asymptotic behaviors of that equation in normed spaces. Moreover, we introduce a new inequality that characterizes the inner product spaces. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the stability problems for the following quadratic functional equation f(x+y+z)+f(x+y-z)+f(x-y+z)+f(-x+y+z) = 4f(x)+4f(y)+4f(z) on an unbounded restricted domain. As a consequence, we can apply the obtained results to obtain some asymptotic behaviors of that equation in normed spaces. Moreover, we introduce a new inequality that characterizes the inner product spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the fixed points of mappings satisfying contractive type condition on a closed ball in an ordered complete dislocated quasi G metric space. The notion of dominated mappings is applied to approximate the unique solution of non linear functional equations. An example is given to show the validity of our work. Our results improve/generalize several well known recent and classical results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some stability results for the following additive-cubic functional equation with an extra term Gf f (2x + y) + f (2x - y) + Gf (x, y) = 2f (x + y) + 2f (x - y) + 2f (2x) - 4f (x). in Banach spaces, where Gf is a functional operator of f. Using these, we give new additive-cubic functional equations and prove their stability. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized Hyers-Ulam stability for the following cubic functional equation f (x + 2y) - 3f (x + y) + 3f (x) - f (x - y) - 6f (y) + Gf (x, y) = 0. with an extra term Gf which is a functional operator of f. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized Hyers-Ulam stability for the following functional equation with an extra term Gf f (x + y) + f (x - y) + Gf (x,y) = 2f (x) + f (y) + f (-y), where Gf is a functional operator of f. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the orthogonally Euler-Lagrange type cubic functional equation f(ax + by) + f(ax - by) - ab²[f(x + y) + f(x - y)] - 2a(a² - b²)f(x) + c[f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y)] = 0; x?y for fixed non-zero rational numbers a; b and a fixed non-zero real number c with a² ≠ b² and a ≠ ±1 and prove the generalized Hyers-Ulam stability for it by using the fixed point method, [ABSTRACT FROM AUTHOR]

Let f : X → Y be a mapping from an orthogonality space (X, ⊥) into a real Banach space (Y, ∥ · ∥). Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally quadratic functional inequality... [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of 3-Lie homomorphisms in 3-Lie algebras for Cauchy-Jensen functional equation. We also prove the Hyers-Ulam stability of 3-Lie derivations on 3-Lie algebras for Cauchy-Jensen functional equation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(2x + y) + f(2x - y) - 6f(x) - 2f(-x) - f(y) - f(-y); t) ≥ N(f(x + y) + f(x - y) - 2f(x) - f(y) - f(-y); kt) for some fixed real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a square root functional equation and a 3rd root functional equation. We prove the Hyers-Ulam stability of the square root functional equation and of the 3rd root functional equation in C*-algebras. [ABSTRACT FROM AUTHOR]

This paper deals with the approximate controllability for a class of semilinear integro-differential functional control equations, which is provided under general sufficient conditions on the system operator, controller and nonlinear terms. Our used tool is applying results similar to Fredholm alternative for nonlinear operators under restrictive assumptions. Finally, a simple example to which our main result can be applied is given. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stability of the Cauchy-Jensen and bi-quadratic functional equation... respectively, in 2-Banach spaces. [ABSTRACT FROM AUTHOR]

Using the mixed point method, we establish some stability results concerning the following new mixed type AQ-functional equation f(-x + 2y) + 2[f(3x - 2y) + f(2x + y) - f(y) - f(y - x)] = 3[f(x + y) + f(x - y) + f(-x)] + 4f(2x - y) in matrix non-Archimedean fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following additive (ρ1, ρ2)-functional in-equalities (0.1) ∥f (x + y + z) - f(x) - f(y) - f(z)∥ ≥ ∥ρ1(f(x + y - z) - f(x) - f(y) + f(z))∥ + ∥ρ2 (f(x - y + z) - f(x) + f(y) - f(z))∥, where ρ1 and ρ2 are fixed complex numbers with |ρ1| ⋅ |ρ2| > 1, and (0.2) ∥f (x + y - z) - f(x) - f(y) + f(z)∥ ≥ ∥ρ1(f(x + y + z) - f(x) - f(y) f(z))∥ + ∥ρ2 (f(x - y + z) - f(x) + f(y) f(z))∥ where ρ1 and ρ2 are fixed complex numbers with |ρ1| > 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

Let f : X → Y be a mapping where X is a quasi-α-normed space and Y is a quasi-β -normed space. The following quadratic functional equation (0.1) ... is introduced and solved by giving its general solution. Moreover, we prove the Hyers-Ulam stability of the functional equation (0.1) by using a direct method. [ABSTRACT FROM AUTHOR]

We introduce a generalized cubic functional equation with an automorphism and investigate the generalized stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-β Banach space by the fixed point of the alternative method. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stability of the Cauchy-Jensen and bi-quadratic functional equation 2f (x + y,z + w/2) = f(x, z) + f(x,w) + f(y, z) + f(y,w), f(x + y, z + w) + f(x + y,z - w) + f(x - y, z + w) + f(x - y, z - w) = 4[f(x, z) + f(x,w) + f(y, z) + f(y,w)], respectively, in 2-Banach spaces. [ABSTRACT FROM AUTHOR]

Recently, stability results of set-valued functional equations on domain of cones in Banach spaces are obtained by several authors. In this paper, we present the refined stability results of set-valued functional equations which is stable in the sense of Aoki, Rassias and Găvrută on domain of cones. [ABSTRACT FROM AUTHOR]

Using the fixed point method, we establish some stability results concerning the following new mixed type AQ-functional equation f(-x + 2y) + 2[f(3x - 2y) + f(2x + y) - f(y) - f(y - x)] = 3[f(x + y) + f(x - y) + f(-x)] + 4f(2x - y) in matrix non-Archimedean fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

Let f : X → Y be a mapping where X is a quasi-α-normed space and Y is a quasi-β-normed space. The following quadratic functional equation Σni=1 f (Σnj=1 j≠i xj + 2 - n/2 xi ) = n2/4 Σn i=1 f(xi), (n ≥ 3) (0.1) is introduced and solved by giving its general solution. Moreover, we prove the Hyers-Ulam stability of the functional equation (0.1) by using a direct method. [ABSTRACT FROM AUTHOR]

We introduce a generalized cubic functional equation with an automorphism and investigate the generalized stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-β Banach space by the fixed point of the alternative method. [ABSTRACT FROM AUTHOR]

Let... We solve the additive-quadratic ƿ-functional equations...and... where ƿ is a fixed nonzero number with ƿ 6= 1. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ƿ-functional equations (0.1) and (0.2) in β-homogeneous F-spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of a Menger probabilistic normed Riesz space. We study some properties of these spaces and compare normed Riesz spaces with Menger probabilistic normed Riesz spaces. Next, we investigate the Hyers-Ulam stability of lattice homomorphisms in Menger probabilistic normed Riesz spaces. [ABSTRACT FROM AUTHOR]

In the current work, using the fixed point theorems due to Brzdȩk and Ciepliński, we give some Ulam-Hyers stability results for the decic functional equation in non-Archimedean spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of the following additive functional equation ... in fuzzy Banach spaces, where m is a positive integer greater than 3. [ABSTRACT FROM AUTHOR]

Using the fixed point alternative theorem, we investigate the Hyers-Ulam stability of of n-Jordan *-derivations on induced fuzzy C*-algebras associated with the following functional equation f (my - x) + f (x - mz) + mf (x - y + z) = f (mx), where m is a fixed integer greater than 1. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of the following additive functional equations f (x+y/2 + z + w) = 1/2 f(x) + 1/2 f(y) + f(z) + f(w), f (x+y+z/3 + w) = 1/3 f(x) + 1/3 f(y) + 1/3 f(z) + f(w) in paranormed spaces. [ABSTRACT FROM AUTHOR]

Using the fixed point alternative theorem, we investigate the Hyers-Ulam stability of of n-Jordan *-derivations on induced fuzzy C*-algebras associated with the following functional equation f (x - y + z) + f (x - z) + f (2x + y) = f (4x). [ABSTRACT FROM AUTHOR]

In this paper, we study the septendecic functional equation and prove the Hyers-Ulam stability for the septendecic functional equation in matrix normed spaces by using the fixed point technique. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this note, the notion of a mixed weakly monotone pair of mappings is invoked to prove some coupled common fixed point theorems in partially ordered b-metric spaces. Results proved in this note are authenticated by some innovative examples. Demonstrative surfaces leading to better understanding of calculation done. Moreover as an application our results are utilized to establish existence of solutions of system of integral equations which is also substantiated by an example. [ABSTRACT FROM AUTHOR]

Recently, stability results of set-valued functional equations on domain of cones in Banach spaces are obtained by several authors. In this paper, we present the refined stability results of set-valued functional equations which is stable in the sense of Aoki, Rassias and Găvrută on domain of cones. [ABSTRACT FROM AUTHOR]

Using the fixed point method, we establish some stability results concerning the following new mixed type AQ-functional equation f(-x + 2y) + 2[f(3x - 2y) + f(2x + y) - f(y) - f(y - x)] = 3[f(x + y) + f(x - y) + f(-x)] + 4f(2x - y) in matrix non-Archimedean fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we introduce and solve the following additive (ρ1; ρ2)-functional in- equalities ‖ (x + y + z) - f(x) - f(y) - f(z)‖ ≥ kρ,1(f(x + y - z) - f(x) - f(y) + f(z))‖ +‖ρ,2 (f(x - y + z) - f(x) + f(y) - f(z))‖ , (0.1) where ρ1 and ρ,2 are fixed complex numbers with |ρ1| • |ρ,2| > 1, and ‖ (x + y - z) - f(x) - f(y) + f(z)‖ ≥ ‖ρ,1(f(x + y + z) - f(x) - f(y) - f(z))‖ +‖ρ2 (f(x - y + z) - f(x) + f(y) - f(z))‖ (0.2) where ρ,1 and ρ,2 are fixed complex numbers with |ρ1| > 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (ρ1, ρ,2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

Let f : X → Y be a mapping where X is a quasi-α-normed space and Y is a quasi-β-normed space. The following quadratic functional equation Σni=1 f (Σnj=1 j≠i xj + 2 - n/2 xi ) = n2/4 Σn i=1 f(xi), (n ≥ 3) (0.1) is introduced and solved by giving its general solution. Moreover, we prove the Hyers-Ulam stability of the functional equation (0.1) by using a direct method. [ABSTRACT FROM AUTHOR]

We introduce a generalized cubic functional equation with an automorphism and investigate the generalized stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-β Banach space by the fixed point of the alternative method. [ABSTRACT FROM AUTHOR]

Let .... We solve the additive-quadratic ρ-functional equations (0.1) M1f (x, y) = ρM2f(x, y) and (0.2) M2f (x, y) = ρM1f (x, y), where ρ is a fixed nonzero number with ρ ≠ 1. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional equations (0.1) and (0.2) in β-homogeneous F-spaces. [ABSTRACT FROM AUTHOR]

In this paper, some notions are introduced in modular metric spaces. Next some common fixed points are established in ω-orbitally complete modular metric spaces by employing C-class functions that extend and generalize the results of [10,18]. Finally, for usibility of our results an application is provided to show the existence of solutions for certain system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following quadratic ρ-functional inequalities ..., where ρ is a fixed complex number with |ρ| < 1/8, and ..., where ρ is a fixed complex number with |ρ| < 4. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In the current work, using the fixed point theorems due to Brzdęk and Ciepliński, we give some Ulam-Hyers stability results for the decic functional equation in non-Archimedean spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of the following additive functional equations ... in paranormed spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following quadratic (ρi, ρ2)-functional inequalities ..., where ρ1 and ρ2 are fixed nonzero complex numbers with |ρ1|/2 + |p2| < 1, and ..., where ρ1 and ρ2 are fixed nonzero complex numbers with |ρ1|/2 + 2|p2| < 1. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ1, ρ2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

Using the fixed point alternative theorem, we investigate the Hyers-Ulam stability of of n-Jordan *-derivations on induced fuzzy C*-algebras associated with the following functional equation f (my - x) + f (x - mz) + mf (x - y + z) = f (mx), where m is a fixed integer greater than 1. [ABSTRACT FROM AUTHOR]