Search

In this paper, we introduce the following new additive s-functional inequalities ||f(x - y) + f(y) + f(-x)|| ≤ ||s (f(x + y) - f(x) - f(y)) k; (0.1) ||kf(x + y) - f(x) - f(y)|| ≤ ||s (f(x - y) + f(y) + f(-x)) k; (0.2) where s is a fixed complex number with |s| < 1, and prove the Hyers-Ulam stability of linear derivations on Banach algebras associated to the additive s-functional inequalities (0.1) and (0.2). [ABSTRACT FROM AUTHOR]

In this paper, we show the Ulam-Hyers stability and Ulam-Hyers-Rassias stability criterion for nonlinear Hadamard fractional relaxation differential equations on compact and unbounded time intervals. More explicit Ulam-Hyers stability and Ulam-Hyers-Rassias results are presented by virtue of estimation of Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

The "oldest quartic" functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x - 2y) = 4[f(x + y) + f(x - y)] - 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic functional equations, and establish fundamental formulas for the general solution of such functional equations and for "Ulam stability" of pertinent quartic functional inequalities. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the existence, uniqueness and stability of solution for stochastic functional differential equations driven by G-Brownian motion (in short G-SFDEs). The existence-and-uniqueness theorem is established for G-SFDEs under non-Lipschitz condition and weakened linear growth condition. We have used the Picard approximation scheme, Gronwall's inequality, Bihari's inequality and Burkholder-Davis-Gundy (in short BDG) inequalities to develop the existence theory for the above mentioned stochastic dynamical systems. In addition, the mean square stability of solutions for these systems has been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the generalized Hyers-Ulam stability of the additive functional inequality ‖(ax + by + cz) + f(bx + ay + bz) + f(cx + cy + az)‖ ≤ ‖(a + b + c)f(x + y + z)‖ in vector Banach space, where a ≠ b ≠ c 2 R are fixed points with 3 > ∣a + b + c∣. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive p-functional inequalities ... in fuzzy normed spaces, where p is a fixed real number with |ρ| < 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive p-functional inequalities (0.1) and (0.2) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the quadratic ρ-functional inequalities ... where ρ is a fixed non-Archimedean number with |ρ| < 1/2. Furthermore, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in non-Archimedean 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 non-Archimedean Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive-quadratic ρ-functional inequalities ... where ρ is a fixed complex number with |ρ| < 1, and ... where p is a fixed complex number with |p| < 1/2, and prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) and (0.2) in β-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive-quadratic p-functional equations associated with the additive-quadratic p-functional inequalities (0.1) and (0.2) in β-homogeneous complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following cubic p-functional inequality Il f (2x + y) + f (2x - y) - 2f (x + y) - 2f (x - y) - 12f (x)|| where p is a fixed complex number with | ρ| < 2, and the quartic ρ-functional inequality ||f (2x + y) + f (2x - y) - 4 f (x + y) - 4f (x - y) - 24f (x) + 6f(y)||... where ρ is a fixed complex number with | ρ| < 2. Using the direct method, we prove the Hyers-Ulam stability of the cubic ρ-functional inequality (0.1) and the quartic ρ-functional inequality (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

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

In this paper, we solve the quadratic ρ-functional inequalities... where ρ is a number with |ρ| < 1 and ... where ρ is a number with |ρ| < 1/2 2. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in normed spaces. [ABSTRACT FROM AUTHOR]

In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; κ) quadratic mapping. The other authors of this research area have established important results also on functional inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a positive-additive functional equation in fuzzy C*-algebras. Using fixed point methods, we prove the stability of the positive-additive functional equation in fuzzy C*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the following additive functional inequality: N(f(x) + f(y) + f(z) + f(w), t) ≥ N(f(x) + f(y + z + w), t) in fuzzy normed modules over a fuzzy C*-algebra, which is applied to understand homomorphisms in fuzzy C*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a positive-additive functional equation in fuzzy C*-algebras. Using fixed point methods, we prove the stability of the positive-additive functional equation in fuzzy C*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the following additive functional inequality: ... in fuzzy normed modules over a fuzzy C*-algebra, which is applied to understand homomorphisms in fuzzy C*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of inner product preserving mappings in Hilbert spaces for the following additive functional equation f(ax + by) = af(x) + bf (y). [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality ||f(3x + 2y + z) + f(x + 2y + 2z) + f(2x + 2y + 3z)|| ≤ ||6f(x + y + z)|| in Banach spaces [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability problem for the following function inequalities ... in β-homogeneous F-spaces. [ABSTRACT FROM AUTHOR]