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In the paper, we study dynamic h-convexity for interval valued functions. Some generalizations of Jensen's inequality in interval valued analysis for h-convex functions on time scales are proved in the paper. In seek of applications of generalized Jensen's inequality, Hermite-Hadamard type inequalities for h-convex functions on time scales are established. Further discrete analogues of newly proved results are also presented in the paper. Some numerical examples are also provided to check the validity of the results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of strongly generalized convex functions which is called as strongly η-convex stochastic processes. We prove the Hermite-Hadamard, Ostrowski type inequality, and obtain some important inequalities for above processes. Some previous results are special cases of the results obtained in this paper. [ABSTRACT FROM AUTHOR]

The class of geometrically convex functions is a rich class that contains some important functions. In this paper, we further explore this class and present many interesting new properties, including fundamental inequalities, supermultiplicative type inequalities, Jensen-Mercer inequality, integral inequalities, and refined forms. The obtained results extend some celebrated results from the context of convexity to geometric convexity, with interesting applications to numerical inequalities for the hyperbolic and exponential functions. [ABSTRACT FROM AUTHOR]

The widely known hermite-hadamard-Fejer type inequalities are so important in the field of mathematical analysis. Many researchers have studied on these inequalities. In this paper, we have obtained several inequalities related to the Hermite-Hadamard inequality for a special class of the functions called uniformly convex functions. We have also presented applications of these obtained inequalities in some error estimates for higher moments of random variables. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents new simple lower and upper bounds for the cumulative normal distribution function, Φ(z). The accuracy and closeness of the proposed bounds to the exact Φ(z) are investigated based on the maximum absolute error and the mean absolute error. It is found that the maximum absolute error of the proposed lower bound is 8.55×10−3 and it is 4.1×10−4 for the upper bound. In addition, based on 5001 values between z=0 and z=5 with step 0.001, we found that the mean absolute error is 3.27×10−3 for the lower bound and it is 1.1×10−4 for the upper bound and these two values decrease with increasing the z value. [ABSTRACT FROM AUTHOR]

In this paper, we prove the boundedness of Hardy operator for monotone functions in grand Lebesgue spaces Lp)(0, 1) (0 < p ≤ 1). In particular, we prove similar results for the Hardy operator in weighted Lebesgue spaces. Also, it is proved that the grand Lebesgue space Lp)(0, 1) is a quasi-Banach function space. Finally, we establish necessary and sufficient conditions for the boundedness of some integral operator in weighted quasi-Banach Lebesgue spaces. [ABSTRACT FROM AUTHOR]

This paper presents a general theorem dealing with absolute Cesàro summability of the series ∑ a n λ n under weaker conditions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some properties of the domains ℓ p (Γ n) , c 0 (Γ n) , c (Γ n) and ℓ ∞ (Γ n) of the Gamma matrix of order n in the classical spaces ℓ p , c0, c and ℓ ∞ of absolutely p-summable, null, convergent and bounded sequences, respectively, and compute the α-, β- and γ-duals of these spaces. We characterize the classes of infinite matrices from the space ℓ p (Γ n) to the spaces ℓ ∞ and f, and from a normed sequence space to the gamma sequence spaces ℓ p (Γ n) , c 0 (Γ n) , c (Γ n) and ℓ ∞ (Γ n). Moreover, we introduce the necessary and sufficient conditions for factorizing an operator based on the weighted mean matrices and derive the factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Finally, we emphasize on the lower bound of operators from ℓ p into ℓ p (Γ n) , from ℓ p (Γ n) into ℓ p , from ℓ p (Γ n) into itself and from ℓ p into itself. [ABSTRACT FROM AUTHOR]

This paper is devoted to novel diamond alpha Hardy–Copson type dynamic inequalities, which are ζ < 0 complements of the classical ones obtained for ζ > 1 , and their applications to difference equations. We obtain two kinds of diamond alpha Hardy–Copson type inequalities for ζ < 0 , one of which is mixed type and established by the convex linear combinations of the related delta and nabla inequalities while the other one is new and is obtained by using time scale calculus rather than algebra. In contrast to the works existing in the literature, these complements are derived by preserving the directions of the classical inequalities. Therefore both kinds of our results unify some of the known delta and nabla Hardy–Copson type inequalities obtained for ζ < 0 into one diamond alpha Hardy–Copson type inequalities and offer new types of diamond alpha Hardy–Copson type inequalities which have the same directions as the classical ones and can be considered as complementary inequalities. Moreover the application of these inequalities in the oscillation theory of half linear difference equations provides several nonoscillation criteria for such equations. [ABSTRACT FROM AUTHOR]

In this paper, the concept of a convex function with respect to a pair of functions is introduced. Then some properties related to this notion are established. Furthermore, some fundamental inequalities from the theory of convex functions are extended to this new class of mappings. [ABSTRACT FROM AUTHOR]

In this paper, we give refinements for the G-majorization triangle inequality (x + y) ↓ ≺ G x ↓ + y ↓ with vectors x , y of an Eaton triple and normal map (⋅) ↓ . For instance, we establish refinements for the majorization Ky Fan's eigenvalue inequality λ (x + y) ≺ m λ (x) + λ (y) with Hermitian matrices x and y and the eigenvalue operator λ (⋅). Likewise, we show refinements for the weak majorization Ky Fan's singular value inequality s (x + y) ≺ w s (x) + s (y) with complex matrices x and y, where s (⋅) stands for the singular values operator. In particular, we recover original Maligranda's refinement of the norm triangle inequality. [ABSTRACT FROM AUTHOR]

In this paper, a new identity is established for differentiable mappings. By using the mathematical analysis techniques, some new integral inequalities of Hermite-Hadamard type for differentiable p-convex functions are proved. A comparison of the established results with previously obtained results is demonstrated to show that the results presented in this paper are better than those already exist in literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider thequadratic weighted geometric mean for bounded linear operatorsT, Vin the Hilbert spaceHwithTinvertible and. Using the celebrated McCarthy’s inequality we show that for anywherep, withWe also provide some norm inequalities such as for anyn-tuples of invertible operatorsand anyn-tuple of positive weights. [ABSTRACT FROM PUBLISHER]

In this paper, a Cauchy problem of Helmholtz equation in a multi-dimensional case is investigated. This problem is severely ill-posed and small perturbations to measurement data can result in large changes in the solution. A kind of operator regularization method is proposed. The stable error estimates are obtained in the L 2 − norm and H r − norm under the conditions that m is even, md>x, mk>1, and suitable choice of regular parameters. Error estimates show that the regularized solution depends continuously on the perturbation noisy data and wave number. Our method makes up the limitation of small waves. Three numerical experiments show that our proposed method is effective and stable, especially in the case of a large wave number. [ABSTRACT FROM AUTHOR]

Based on a known sharpened and refined versions of a classical Steffensen inequality, we derive new sharpened and refined versions of a q–Steffensen inequality. Next, we give weaker conditions for some already known generalizations of q–Steffensen's inequality and for new refinements obtained in this paper. [ABSTRACT FROM AUTHOR]

The use of Haar wavelet analysis, instead of classical trigonometric analysis, provides inequalities which can be regarded as Heisenberg-type inequalities associated to fractional order quantum mechanics. The aim of this paper is to introduce and prove some of these lower order uncertainty estimates. [ABSTRACT FROM AUTHOR]

In the present paper, we have proved a basic theorem on the absolute Riesz summability factors of infinite series by using a wider class of power increasing sequences and then we applied this new result to the trigonometric Fourier series. Some new results are also obtained concerning the factored infinite series and trigonometric Fourier series. [ABSTRACT FROM AUTHOR]

Let Δ − n be the backward difference operator of order −n. In this paper, we study some properties of the matrix domain associated with this operator and after computing α-, β-, γ-duals, we characterize some matrix classes on this space. Moreover, we investigate the problem of finding the norm of well-known operators such as Cesàro and Hilbert from ℓ p (Δ − n) into ℓ p. [ABSTRACT FROM AUTHOR]

In this paper, two Cauchy problems of Helmholtz equation in a three-dimensional case are considered. To address these problems, a mollification method with bivariate Dirichlet kernel is proposed. Stable errors estimates are obtained based on appropriate a priori choices of mollification parameters. Convergence estimates show that the regularization solution depends continuously on the data and wavenumber. Numerical examples of our interest show that Dirichlet kernel is more effective than the Gaussian kernel under the same parameter selection rule, and our procedure is stable with respect to perturbations noise in the data. [ABSTRACT FROM AUTHOR]

In this paper, firstly we proved a general theorem dealing with absolute Riesz summability factors of infinite series under weaker conditions. And secondly we applied it to the trigonometric Fourier series. Also we have obtained some new and known results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce factorizations for the Hilbert and Cesàro matrices based on generalized Cesàro matrix and as the application, we generalize the Hardy's inequality versus Hilbert's. [ABSTRACT FROM AUTHOR]

The utilisation of Management information system has grabbed the attention since last decades. The selection of management sources is a difficult assignment for decision-experts. Thus, the present article develops a new technique using entropy measures and a novel extended VIKOR-TODIM model of Intuitionistic Fuzzy Sets. A new parametric entropy measure based on Havrda–Charvat–Tsallis entropy for a probability distribution is proposed and discussed their particular cases. Some properties of this measure has been proved mathematically. A comparison of proposed entropy measure with several existing entropy measures is shown to demonstrate the consistency of the proposed approach. In this paper, we proposed an integrated approach based on VIKOR and TODIM and entropy-weighted method for solving multi-criteria decision-making problems under intuitionistic fuzzy environment and the criteria weights are partial known. Firstly, the problem with multi-criteria decision-making is designed and the steps, principles of the proposed VIKOR-TODIM method are presented. Finally, to verify the applicability and feasibility of the proposed approach, a problem of management information system in a teaching hospital is presented and compared the results with other existing methods. The present work demonstrated, that the proposed VIKOR-TODIM is effective to select and evaluate management information system in any organisation. [ABSTRACT FROM AUTHOR]

This paper deals with a brief history of the most remarkable Euler numberse, i and γ in mathematical sciences. Included are many properties of the constantse, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce the notion of coordinated harmonically convex functions. We derive some new integral inequalities of Hermite–Hadamard type for coordinated Harmonically convex functions. The interested readers are encouraged to find the applications of harmonically convex functions in pure and applied sciences. [ABSTRACT FROM AUTHOR]

Letandbe a non-negative matrix. Denote by, the supremum of those, satisfying the following inequalitywhereis a partition of positive integers,,is a non-negative sequence inandis a monotone and non-negative sequence of real number. In this paper a Hardy-type formula is obtained for, whereis the generalized Hausdorff matrix,andAnother purpose of this paper is to establish a general upper estimate for the exact value of, for which recently a lower estimate was established in Lashkaripour and Talebi [Lashkaripour R, Talebi G. Bull. Iran. Math. Soc. 2011;37:115–126], whereis a non-negative lower triangular matrix and. We also derive the corresponding result forwithIn particular, we apply our results to summability matrices, weighted mean matrices, Nörlund matrices. Our results also generalize some results in Chen and Wang [Chen C-P, Wang K-Z. Linear Multilinear Algebra, March 2011;59:321–337] and Lashkaripour and Talebi [Lashkaripour R, Talebi G. Czech. Math. J. 2012; 62: 293–04.]. [ABSTRACT FROM AUTHOR]

In this paper, the weighted norm inequalities of the following special type of integral operators are investigated: whereor. In particular, those established by E. T. Copson, Hardy-Littlewood-Pólya, S. Lai, N. Levinson, E. R. Love, B. G. Pachpatte and Yang-Hwang will be derived. [ABSTRACT FROM AUTHOR]

In this paper, we have proved a general theorem dealing with the ϕ −| C, α, β |k summability factors of infinite series. Also, some new and known results are deduced. [ABSTRACT FROM AUTHOR]

Letbe a non-negative matrix. Denote by, the infimum of thosesatisfying the following inequality: where,andis the Fibonacci numbers sequence andis a decreasing, non-negative sequence of real numbers. In this paper, first, the Fibonacci weighted sequence spaceis introduced. Then, we focus on the evaluation of, whereis the Hausdorff matrix operator or the Nörlund matrix operator or the transpose of the Nörlund matrix operator. For the case of Hausdorff matrices, a Hardy-type formula is established as an upper estimate. Also, a general upper estimate is established for the case of Nörlund matrices and their transpose. In particular, we apply our results to Cesàro matrices, Hölder matrices, Euler matrices and Gamma matrices. [ABSTRACT FROM AUTHOR]

In the present paper, a new theorem concerning absolute matrix summability factors, which generalizes a theorem on the summability factors of infinite series, has been proved by using almost increasing sequence and matrix transformation. [ABSTRACT FROM AUTHOR]

In this paper, we have proved a known theorem dealing with ϕ — |C, α|k summability factors of infinite series under more weaker conditions. Also, some new results are obtained. [ABSTRACT FROM AUTHOR]

The paper deals with a general class of linear positive approximation processes designed using series. For continuous and bounded functions defined on unbounded interval we give rate of convergence in terms of the usual modulus of smoothness. The main goal is to identify functions for which these operators provide uniform approximation over unbounded intervals. Particular cases are delivered. [ABSTRACT FROM AUTHOR]

In a recent paper [19], the authors obtained a sharp version of the Trudinger-Moser inequality in the whole space ℝ2, giving necessary and sufficient conditions for the boundedness and the compactness of general nonlinear functionals inW1, 2(ℝ2). We complete this study showing that an analogue of the result in [19] holds in arbitrary dimensions N ≥2. We also provide an application to the study of the existence of ground state solutions for quasilinear elliptic equations in ℝN. [ABSTRACT FROM AUTHOR]

Letbe a non-negative matrix. Denote by, the infimum of thosesatisfying the following inequality:where,andis a decreasing, non-negative sequence of real numbers. In this paper, first the Euler weighted sequence spaceis introduced. Then we focus on the evaluation of, whereis the Hausdorff matrix operator or the Nörlund matrix operator. For the case of Hausdorff matrices, a Hardy type formula is established as an upper estimate. Also, a general upper estimate is established for the case of Nörlund matrices. Our results not only generalize some work of Altay, Basàr and Mursaleen but also provide some analogue to those given by Bennett, Johnson and Foroutannia. [ABSTRACT FROM PUBLISHER]

This paper deals with various weighted inequalities for the forward difference operator acting on products of compositions and convolutions of functions on. A discrete version of Saitoh's inequality in the Sobolev space and some generalizations of discrete Opial-type inequalities are considered. Several applications to the zeta functions and difference equations are also given. [ABSTRACT FROM AUTHOR]

It is well known that ifXr: nandYr: nare order statistics from the i.i.d. samples with distribution functions F and G, respectively, such that F succeeds G in the convex order then. The result was extended to the generalized order statistics, and is also valid for their convex combinations. In this paper, we show that analogous relations hold true for much larger classes of linear combinations of generalized order statistics. [ABSTRACT FROM PUBLISHER]

In this paper, we establish the Muckenhoupt-type estimation for the best constantassociated with the following multidimensional modular inequality over a spherical cone:whereand. Similar results are also derived for the complementary integral operator. Our results provide the-dimensional modular forms of the works of Andersen and Heinig. As consequences of our results, we give the-dimensional weighted extensions of Levinson modular inequality, extensions of Stepanov and Heinig results, generalizations of the Hardy–Knopp-type inequalities, and those for the Riemann–Liouville operator and the Weyl fractional operator. We also point out that our estimates are better than those given in the works of Drabek, Heinig, Kunfer, and Sinnamon. [ABSTRACT FROM PUBLISHER]

In this paper we give extensions of Opial-type integral inequalities and use them to obtain a generalization of an inequality due to Agarwal and Pang. Applications with respect to fractional derivatives and fractional integrals are also given. [ABSTRACT FROM PUBLISHER]

In this paper, we initially present new some inequality of Hermite–Hadamard-type for co-ordinated convex functions on a rectangle from the plane ℝ2via Riemann–Liouville fractional integrals. Then, we give an integral identity for fractional integrals and with the help of this integral identity we establish some integral inequalities with the right-hand side of the fractional Hermite–Hadamard-type inequality on the co-ordinates. [ABSTRACT FROM PUBLISHER]

On utilizing a refinement and a reverse of Young's inequality, in this paper, we establish new inequalities for functions defined by power series with positive coefficients, which improve the famous Hölder's inequality for power series. Some applications for special functions such as polylogarithm, hypergeometric and Bessel functions are presented as well. [ABSTRACT FROM PUBLISHER]

In this paper, we derive new inequalities for power series with real coefficients and apply them for some complex functions of interest such as exponential, trigonometric, hypergeometric, polylogarithm and Bessel functions [ABSTRACT FROM AUTHOR]

In this paper, we have extended a known theorem dealing with | , pn|k summability factors to the |A, pn|k summability under weaker conditions by using an almost increasing sequence [ABSTRACT FROM AUTHOR]

An infinite homogeneous [image omitted] -dimensional medium initially is at zero temperature. A heat impulse is applied at the origin, raising the temperature at the observation point [image omitted] to a value greater than a constant value [image omitted] . The temperature there then decays and when it reaches [image omitted] at time [image omitted] , another equal-sized heat impulse is applied at the origin. Subsequent equal-sized heat impulses are applied at the origin at times [image omitted] , when the temperature at the observation point [image omitted] has decayed to [image omitted] . This sequence [image omitted] of heating times can be defined recursively by a difference equation and its asymptotic behaviour is studied in this paper. A similar heat conduction problem in which the observation point is set at the origin was first studied by Myshkis in Journal of Difference Equations and Applications 3 (1997), 89-91. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new discrete Gronwall-Bellman-Ou-Iang type inequalities over 2-dimensional lattices. These, on one hand, generalize some existing results in the literature and on the other hand, provide a handy tool for the study of qualitative properties of solutions of difference equations. We illustrate this by applying these new results to certain boundary value problem for difference equations. [ABSTRACT FROM AUTHOR]

In this note, we study the so-called Hermite-Hadamard inequality for the class of subharmonic functions. We first prove an inequality of this type for subharmonic functions over circular ring domains. Next, a new Hermite-Hadamard-type inequality over a disk is deduced. Moreover, we introduce the class of subharmonic functions on the coordinates, which includes the class of convex functions on the coordinates, and establish several new integral inequalities for this class of functions over various product domains: product of disks, product of circular rings and product of a disk and a circular ring. [ABSTRACT FROM AUTHOR]

In this paper, we present a variety of integral inequalities in Lp and Lp,r spaces for the integral operator involving generalized Mittag-Leffler function in its kernel, Hilfer fractional derivative, generalized Riemann-Liouville and Riemann-Liouville k-fractional integral operators. [ABSTRACT FROM AUTHOR]

For weighted Hardy and Cesàro operators on Heisenberg group, we give the exact values for its norms in Morrey space, its central variant and. Also we prove the sharp two-sided estimate for its norm in Herz space. These statements are analogues of results due to Z.W.Fu and S.Z.Lu (Morrey and Herz spaces), S.S.Volosivets (BLOspace) and generalize previous result concerningspace by Chu et al. [ABSTRACT FROM PUBLISHER]

In the paper, the authors introduce a new concept "extended ((s1, m1)-(s2, m2))-convex function on co-ordinates" and establish some new inequalities of the Hermite-Hadamard type for extended ((s1, m1)-(s2, m2))-convex functions of 2 variables on co-ordinates. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce definitions of the (h1, h2)-GA-convex functions and the (h1, h2, m)-GA-convex functions, discuss some properties of these kinds of functions, establish some integral inequalities for these functions, and apply these inequalities to construct several more inequalities. [ABSTRACT FROM AUTHOR]

For a positive trace-class operator C and a bounded operator A, we provide an explicit description of the closure of the orbit-closed C-numerical range of A in terms of those operators submajorized by C and the essential numerical range of A. This generalizes and subsumes recent work of Chan, Li and Poon for the k-numerical range, as well as some of our own previous work on the orbit-closed C-numerical range. [ABSTRACT FROM AUTHOR]

We introduce and investigate the orbit-closed C-numerical range, a natural modification of the C-numerical range of an operator introduced for C trace-class by Dirr and vom Ende. Our orbit-closed C-numerical range is a conservative modification of theirs because these two sets have the same closure and even coincide when C is finite rank. Since Dirr and vom Ende's results concerning the C-numerical range depend only on its closure, our orbit-closed C-numerical range inherits these properties, but we also establish more. For C self-adjoint, Dirr and vom Ende were only able to prove that the closure of their C-numerical range is convex and asked whether it is convex without taking the closure. We establish the convexity of the orbit-closed C-numerical range for self-adjoint C without taking the closure by providing a characterization in terms of majorization, unlocking the door to a plethora of results which generalize properties of the C-numerical range known in finite dimensions or when C has finite rank. Under rather special hypotheses on the operators, we also show the C-numerical range is convex, thereby providing a partial answer to the question posed by Dirr and vom Ende. [ABSTRACT FROM AUTHOR]