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In this paper, we introduce and solve the following additive (ρ1; ρ2)-functional in- equalities ‖ (x + y + z) - f(x) - f(y) - f(z)‖ ≥ kρ1(f(x + y - z) - f(x) - f(y) + f(z))‖ +‖ρ2 (f(x - y + z) - f(x) + f(y) - f(z))‖ , (0.1) where ρ1 and ρ2 are fixed complex numbers with |ρ1| • |ρ2| > 1, and ‖ (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))‖ (0.2) where ρ1 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, ρ2)-functional inequalities (0.1) and (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper we establish some equalities and inequalities for K-g-frames. Our results generalize the remarkable results obtained by Balan et al. and Găvruţa. We also give several new inequalities for K-g-frames by using operator theory methods, which differ in structure from those for frames. [ABSTRACT FROM AUTHOR]

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)) ‖; (0.1) ‖f(x + y) - f(x) - f(y)‖ ≤ ‖s (f(x - y) + f(y) + f(-x)) ‖; (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]

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]

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 fi rstly establish the second main theorem about meromorphic functions on annuli concerning small functions. Then, by using this theorem, we deal with the uniqueness of meromophic functions sharing some small functions on annuli and obtain the results of meromporphic functions sharing five small functions on annuli, which is an answer to the question of Cao and Yi. In addition, we investigate the properties of meromorphic functions on annuli, and obtain a form of Yang's inequality on annuli by reducing the coeffcients of Hayman's inequality. Moreover, we also study Hayman's inequality in different forms, and obtain accurate estimates of sums of de ficiencies. [ABSTRACT FROM AUTHOR]

In this paper, we study the Heinz mean inequalities of two positive operators involving positive linear map. We obtain a generalized conclusion based on operator Diaz-Metcalf type inequality. The conclusion is presented as follows: Let Φ be a unital positive linear map, if 0 < m1 2 ≤ A ≤ M1 2 and 0 < m2 2 ≤ B ≤ M22 for some positive real numbers m1 ≤ M1, m2 ≤ M2, then for α ϵ [0; 1] and p ≥ 2, the following inequality holds : ( M2m2/ M1m1 Φ(A) + Φ(B))p ≤2-(p+4) [M2m2(M1 2 + m1 2) +M1m1(M2 2 + m2 2) /min{(M1m1) 3-α/2 (M2m2) 1+α/2, (M1m1) 2+α/2 (M2m2)2-α/2}2p Φp(Hα(A;B)). [ABSTRACT FROM AUTHOR]

In the paper, we prove that the Bateman's G--function satisfies the double inequality Σ2m n=1 (2n-1)B2n/nx2n < G(x) - 1/x < Σ2m-1 n=1 (2n-1)B2n/nx2n , m ∊ N with best bounds, where B'rs are the Bernoulli numbers and we study the monotonicity of some functions involving the function G(x). Also, we present some estimates for the error term of a class of the alternating series, which improve and generalize some recent resutls and we prove the increasing monotonicity of a sequence arising from computation of the intersecting probability between a plane couple and a convex body. [ABSTRACT FROM AUTHOR]

In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in [6, 7] and a generalized Mortici's lemma. [ABSTRACT FROM AUTHOR]

In this paper,we have established some Hermite-Hadamard in-equalities for preinvex functions via fractional integrals and these results have some relationship with the obtained results. Application of the obtained results are given as well. [ABSTRACT FROM AUTHOR]

In the paper, we present the following double inequality ... where ... is the q--gamma function and Wn,q is the q--Wallis ratio. 2010 Mathematics Subject Classification: 05A10, 33D05, 26D20. [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 inqualities to derive some inqualitites of special means. [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]