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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]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem... is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that ƒ(t; x; y; z) may be superlinear or sublinear growth on x, y and z as |(x; y; z)| → 0 and |(x; y; z)| → ∞. [ABSTRACT FROM AUTHOR]

In this paper we are interested to give the Hadamard inequality for n-times differentiable convex functions via Caputo fractional derivatives. We also find bounds of a difference of this inequality. [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]

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]

In the present paper, we aim to investigate a new q-integral inequality of Grüss type for the Saigo fractional q-integral operator. Some special cases of our main results are also provided. The results presented in this paper improve and extend some recent results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce set-valued quadratic ρ-functional inequalities and prove the Hyers-Ulam stability of the set-valued quadratic ρ-functional inequalities by using the fixed point method. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we study the solution to linear matrix inequality AXB + (AXB)*≤ C for Hermitian matrix C. Furthermore, for the applications, we derive the representations for the common Re-nnd solution to equations AX = C and XB = D, and the Re-nnd {1,3,4}-inverse for square matrix. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate the following additiveρ-functional inequalities N(f(x + y + z) - f(x) - f(y) - f(z), t) ⩾ N (ρ(2f(x+y/2+z)-f(x)-f(y)-2f(z)),t) N(2f(x+y/2+z)-f(x)-f(y)-2f(z)),t) ⩾ N (ρ(2f(x+y+z/2)-f(x)-f(y)-f(z)),t), N(f(x+y+z)-f(x)-f(y)-f(z)),t)in fuzzy normed spaces. Furthermore, we prove the Hyers-Ulam stability of the above additive ρ-functional inequalities in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

This paper discusses the approximation by de la Vallée Poussin means Vnf on the unit sphere. Especially, the lower bound of approximation is studied. As a main result, the strong converse inequality for the means is established. Namely, it is proved that there are constants C1 and C2 such that C1ω (f, 1/√n) p ≤ ‖Vnf - f‖p ≤ C2ω (f, 1/√n) p for any p-th Lebesgue integrable or continuous function f defined on the sphere, where ω(f, t)p is the modulus of smoothness of f. [ABSTRACT FROM AUTHOR]

In the paper, we present the following double inequality ... where n ∈ N, 0 < q < 1, Γq(x) is the q-gamma function and Wn,q is the q-Wallis ratio. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inequalities to derive some inequalities of special means. [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]

In the paper, the authors establish a new integral identity and, by this identity and Hölder's inequality, discover some new Hermite-Hadamard type integral inequalities for functions whose third derivatives are (α, m)-convex. [ABSTRACT FROM AUTHOR]