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Roman-Fores (2008) have studied Stolarsky-type inequality for the fuzzy-integral with respect to a fuzzy measure. Recently, Daraby(2012) proved the Stolarsky-type inequality for the pseudo-integral with respect to the Lebesgue measure and gave an open problem: "Does Stolarsky's inequality hold for the Choquet integral?" In this paper, we prove the Stolarsky-type inequality for the Choquet integral with respect to a fuzzy measure. Furthermore, we investigate the Stolarsky-type inequality for the generated Choquet integral with respect to a fuzzy measure. [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 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]

This paper is devoted to study some properties of the class of positive (p, q)-absolutely summing operators from a Banach lattice into a Banach space. We shall obtain a new characterization of such operators and generalize some inequalities on the Köthe Bochner function spaces. [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 the present paper, we obtain coefficient inequalities, inclusion relationships involving neighborhoods, subordination results, properties involving modified Hadamard products and also study majorization properties of certain subclasses of multivalent analytic functions, which are defined by means of a certain linear operator. Some useful consequences our main results are mentioned and their relevance with some of the earlier results are also pointed out. [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]

Several new weighted inequalities connected with Hermite-Hadamard and Fejér type inequalities are established for functions whose derivatives in absolute value are preinvex. The results presented in this paper provide ex- tensions of those given in earlier works. [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]

Roman-Fores (2008) have studied Stolarsky-type inequality for the fuzzyintegral with respect to a fuzzy measure. Recently, Daraby(2012) proved the Stolarsky-type inequality for the pseudo-integral with respect to the Lebesgue measure and gave an open problem: "Does Stolarsky's inequality hold for the Choquet integral?" In this paper, we prove the Stolarsky-type inequality for the Choquet integral with respect to a fuzzy measure. Furthermore, we investigate the Stolarsky-type inequality for the generated Choquet integral with respect to a fuzzy measure. [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]

This paper is devoted to study some properties of the class of positive (p, q)-absolutely summing operators from a Banach lattice into a Banach space. We shall obtain a new characterization of such operators and generalize some inequalities on the Köthe Bochner function spaces. [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]

The main object of this paper is to study some properties of certain subclass of analytic functions in the open unit disc which is defined by the linear operator ..., where Rnf(z) is the Ruscheweyh derivative, Snf(z) the Salagean operator and ... is the class of normalized analytic functions with A1 = A. These properties include a coefficient inequality, distorsion theorem and extreme points of differential operator. We also discuss the boundedness properties associated with partial sums of functions in the class .... [ABSTRACT FROM AUTHOR]

In this paper, we investigate isomorphisms and derivations in real C*-algebras associated with the following generalized additive functional inequality ǁaf(x) + bf(y) + cf(z)ǁ ≤ ǁf(αx + βy + αz)ǁ. (0.1) We moreover prove the Hyers-Ulam stability of homomorphisms and derivations in real C*-algebras associated with the generalized additive functional inequality (0.1). [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 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 study some new inequalities of Hermite-Hadamard's type fractional integral inequalities for functions whose absolute values of second derivatives are convex and concave . The obtained results generalize the existing Hermite-Hadamard type integral inequalities and their application in special means and numerical integration. [ABSTRACT FROM AUTHOR]

This paper addresses the approximation by feed-forward neural networks (FNNs) with sigmoidal active functions on the unit sphere. Firstly, some nice properties of typical logistic function are derived, and the function and its derivatives are taken as active functions to construct spherical FNNs approximation operators, where the spherical Cesáro mean is employed as a key link in constructing the operators. Subsequently, by using spherical quadrature formula and Marcinkiewicz-Zygmund type inequality, the error of the operators approximating continuous spherical function is estimated, and a Jackson type theorem is established by means of the best polynomial approximation. [ABSTRACT FROM AUTHOR]

In this paper, we study some new inequalities of Hermite-Hadamard's type fractional integral inequalities for functions whose absolute values of second derivatives are convex and concave . The obtained results generalize the existing Hermite-Hadamard type integral inequalities and their application in special means and numerical integration. [ABSTRACT FROM AUTHOR]

In this paper, we deduced the following new asymptotic series Hn - ln n ~ γ + + 1/2(n + 1) + 5/12n(n+1) (1 + 1/5n + 1/50/n² - 1/50/n³ + 59/52500/n4 + 437/37500/n5 - ...) which faster converge to the Euler's constant with the increase in the terms considered, where Hn is the harmonic number. Also, we presented the following double inequality 1/2 + 5/12n(1+1/5/n+1/50/n²)/n+1 < Hn - ln n - γ < 1/2 + 5/12n(1+1/5/n)/n+1; n = 1, 2, 3..., which improved some known inequalities of the sequence Hn - ln n - γ. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the double sequence spaces (...(p))2P, (0...(p))2P, (...(p))2PB, (0...(p))2PB, ...(p) and (...(p))2P. The inclusion relations among these spaces are obtained. We also characterize the matrix classes (ℓ2∞(p), 0c2PB), (ℓ2∞(p), c2PB), (ℓ2∞(p), c2P); ((...(p))2PB, c2PB) and ((...(p))2PB, c2PB)reg. Furthermore, we define the statistical core of a real-valued double sequence belonging to the more general class ℓ2∞(p) and study the statistical core inequalities related to this new type of statistical core by using our matrix classes ((...(p))2PB, c2PB) and ((...(p))2PB, c2PB)reg. [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]