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In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate systems of nonhomogeneous coupled linear matrix differential equations. Applying Kronecker products, the vector operator, and matrix convolution product, we obtain explicit formula of the general solution to this system in terms of matrix series concerning exponentials and Mittag-Leffler functions. [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)) 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 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]

In this paper, we investigate systems of nonhomogeneous coupled linear matrix differential equations. Applying Kronecker products, the vector operator, and matrix convolution product, we obtain explicit formula of the general solution to this system in terms of matrix series concerning exponentials and Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

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 the present paper, the notion of MT(r;g,m,φ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT(r;g,m,φ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT(r;g,m,φ)-preinvex functions that are twice diffierentiable via Riemann-Liouville fractional integrals are established. Some applications to special means are also given. These general inequalities give us some new estimates for Hermite-Hadamard type fractional integral inequalities [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 the paper, the authors establish several new inequalities of the Hermite-Hadamard type for functions whose derivatives are extended s-convex in the absolute value and present some applications to special means of positive real numbers. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following quadratic ρ-functional inequalities ‖f (x + y + z/2) + f(x - y - z/2) + f(y - x - z/2) + f(z - x - y/2) -f(x) - f(y) - f(z)‖ ≤ ‖ρ(f(x + y + z) + f(x - y - z) + f(y - x - z) + f(z - x - y) (0.1) -4f(x) - 4f(y) - 4f(z))‖; where ρ is a fixed complex number with |ρ| < 1/8, and ‖f(x + y + z) + f(x - y - z) + f(y - x - z) + f(z - x - y) -4f(x) - 4f(y) - 4f(z)‖ (0.2) ≤ ‖ ρ(f(x + y + z/2) + f(x - y - z/2) + f(y - x - z/2) + f(z - x - y/2) -f(x) - f(y) - f(z))‖ ; 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 this paper, we introduce and solve the following quadratic (ƿ1, ƿ2)-functional inequalities... where ƿ1 and ƿ2 are fixed nonzero complex numbers with... where ƿ1 and ƿ2 are fixed nonzero complex numbers with... Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ƿ1; ƿ2)- functional inequalities (0.1) and (0.2) in complex Banach spaces. [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 investigate q- analogues of Bieberbach- de Branges theorems and Fekete-Szegö inequalities for certain families of q- convex and q- close-to-convex functions. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept "strongly extended (s,m)-convex function" and establish some integral inequalities of Simpson's type for strongly extended (s,m)- convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate systems of nonhomogeneous coupled linear matrix differential equations. Applying Kronecker products, the vector operator, and matrix convolution product, we obtain explicit formula of the general solution to this system in terms of matrix series concerning exponentials and Mittag-Leffler functions. [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]

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]

In this paper, we investigate the functional inequality N(f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y); t) ≥ N(f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x); kt) for some fixed nonzero real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces by fixed point methods. [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]

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 paper, the authors established two best approximation formulas for the Bateman's G-function. Also, they studied the completely monotonicity of some functions involving G(x). Some new inequalities are deduced for the function and its derivative such as 1/2 ln [1 + 2x + a/x2 + 2x + 4/3 ] < G(x + 2) < 1/2 ln [ 1 + 2x + b/x2 + 2x + 4/3 ], x > 0 where a = 3 and b = e4-16/12 are the best possible constants. Our results improve some recent inequalities about the function G(x). [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following quadratic (ρ1, ρ2)-functional inequality ... in fuzzy normed spaces, where ρ1 and ρ2 are fixed nonzero real numbers with ... < 1, and f (0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ1, ρ2)- functional inequality (0.1) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish several new inequalities of the Hermite-Hadamard type for functions whose derivatives are extended s-convex in the absolute value and present some applications to special means of positive real numbers. [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]

The purpose of this paper is to introduce and study a class of new two-step viscosity iteration methods for approximating fixed points of set-valued nonexpansive mappings in CAT(0) spaces. Here, the fixed point is unique solution of a variational inequality with a contraction mapping. Further, we prove strong convergence theorem of the two-step viscosity iterations with some general conditions in a complete CAT(0) space. The presented results improve and unify the corresponding results in the literature. [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 this paper, we are concerned with the existence of positive solutions of the fully third-order boundary value problem ..., where f: [0, 1] x ℝ+ x ℝ+ x ℝ → ℝ is continuous. Some inequality conditions on f to guarantee the existence of positive solution are presented. These inequality conditions allow that f (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 investigate q- analogues of Bieberbach-de Branges theorems and Fekete-Szegö inequalities for certain families of q- convex and q- close-to-convex functions. [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]

In the paper, the authors introduce a new concept "strongly extended (s,m)-convex function" and establish some integral inequalities of Simpson's type for strongly extended (s, m)-convex functions. [ABSTRACT FROM AUTHOR]

In this paper we derive the famous Fekete-Szegö inequality for the class of p--valent non-bazilevič function using differential operator. [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]

In this paper, we solve the quadratic ρ-functional inequalities ‖f(x + y) + f(x - y) - 2f(x) - 2f(y)‖ ≤ ‖ρ(4f (x + y/2) + f (x - y) - 2f (x) - 2f (y)) ‖, where ρ is a fixed non-Archimedean number with ∣ρ∣ < ∣2∣, and ‖4f (x + y/2) + f (x - y) - 2f (x) - 2f(y) ‖ ≤ ‖ρ(f(x + y) + f(x - y) - 2f (x) - 2f (y))‖, where ρ is a fixed non-Archimedean number with ∣ρ∣ < 1. Furthermore, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces. [ABSTRACT FROM AUTHOR]

In the paper, the authors present some functional inequalities for the generalized error function. Concretely speaking, the authors present several inequalities of the generalized error function in terms of the arithmetic, logarithmic, and exponential means, find monotonicity, convexity, and concavity of the generalized error function, and, consequently, derive two Grünbaum type and Turáan type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of a fixed point of a self-mapping T on a Menger PM-space under two constraint inequalities with respect to two partial orders under two kinds of contractive conditions and obtain some new fixed point results. We then present several useful consequences of our main results. We also give examples to show the validity of our main results. [ABSTRACT FROM AUTHOR]

In this paper, some new integral inequalities of Hermite-Hadamard type are presented for functions whose nth derivatives in absolute value are (α,m)-logarithmically convex. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are (α,m)-logarithmically convex functions as special cases. Our results may provide refinements of some results for (α,m)-logarithmically convex functions already exist in the most recent concerned literature of inequalities. [ABSTRACT FROM AUTHOR]

In this paper, operator m-convex and (α,m)-convex function on the co-ordinates are defined, and some new integral inequalities of Hermite-Hadamard type for operator mconvex and (α,m)-convex on the co-ordinates are established. [ABSTRACT FROM AUTHOR]

In this paper, we first prove two Hermite-Hadamard type inequalities for h-preinvex functions via Riemann-Liouville fractional integrals, and then, by introducing an integral identity including the second order derivatives of a given function, we establish some Hermite-Hadamard type inequalities for functions whose second order derivatives are h-preinvex via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

In the paper, the concept of α-logarithmically preinvex function is introduced, and by creating an integral identity involving an n-times differentiable function, some new Hermite-Hadamard type inequalities for α-logarithmically preinvex functions are established. [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 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 present the notion of (g, φh,m) -convex and (g, log φ) -convex dominated function and present some properties of them. Besides, we attain some Hermite-Hadamard-type inequalities for (g, φh,m) -convex and (g, log φ) -convex dominated functions. Our results generalize some findings about Hermite-Hadamard-type inequalities in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive ρ-functional inequalities N ( f(x + y) - f(x) - f(y) - ρ ( 2f ( x + y 2) - f(x) - f(y), t) ≥ t t + φ(x, y) (0.1) and N ( 2f ( x + y 2) - f(x) - f(y) -ρ(f(x + y) - f(x) - f(y)), t) ≥ t t + φ(x, y) (0.2) in fuzzy normed spaces, where ρ is a xed real number with ρ ≠ 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the Gronwall-Bellman type inequalities involving the distributional Henstock-Kurzweil integral. Moreover, an linear differential equation with distributional coefficients is considered as an application. [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]