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Abstract: A generalization of two sharp inequalities in a recent paper by N. Ujević is established. Applications in numerical integration are also given and the results of N. Ujević are revised and improved. [Copyright &y& Elsevier]

In this paper, the sensitivity for non-autonomous discrete systems is investigated. First of all, two sufficient conditions of sensitivity for general non-autonomous dynamical systems are presented. At the same time, one stronger form of sensitivity, that is, cofinite sensitivity, is introduced for non-autonomous systems. Two sufficient conditions of cofinite sensitivity for general non-autonomous dynamical systems are presented. We generalized the result of sensitivity and strong sensitivity for autonomous discrete systems to general non-autonomous discrete systems, and the conditions in this paper are weaker than the correlated conditions of autonomous discrete systems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the manifolds with non-symmetric connection. Using the non-symmetric affine connection and four kinds of differentiation, 5 independent curvature tensors Minčić (1979)  appear. In the general case of a geodesic mapping of two non-symmetric affine connection spaces and , it is impossible to obtain a generalization of the Weyl projective curvature tensor. In the present paper, we study the case when and have the same torsion at corresponding points. We name such a mapping “equitorsion mapping”. In the work Stanković (2010)  we obtained quantities , that are generalizations of the Weyl tensor, i.e. they are invariants based on . Among only is a tensor. Using the another 5 linearly independent curvature tensors, we proved that there exist 3 equitorsion projective tensors. [Copyright &y& Elsevier]

Abstract In this paper a global weak solution of the 3D generalized micropolar equations with any α ≥ 1 and β > 0 corresponding to any L 2 initial data are considered. Actually, weak solutions associated with α ≥ 5 4 and β ≥ 1 are global classical solutions when their initial data are sufficiently smooth. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a two-dimensional generalized finite integral transform method is developed for new analytic bending solutions of orthotropic rectangular thin foundation plates. The vibrating beam functions are adopted as the integral kernels to construct the integral transform pairs. By imposing the transform to the governing equation, utilizing some inherent properties of the beam functions, the title problem is converted to that of solving a system of linear algebraic equations, by which the new analytic solutions are elegantly obtained in a straightforward way. Numerical examples validate the present method as well as the solutions yielded by satisfactory agreement with the literature and finite element analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with the delay dependent dissipativity for a class of nonlinear neutral delay differential equations. By taking into account the influence of the delay, a new dissipativity criterion is derived by using a generalized Halanay’s inequality, which is less conservative than those in the existing literature in some cases. At last, two examples are provided to validate our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we obtain the sufficient conditions for the uniqueness of solutions for a boundary value problem of fractional differential equations involving generalized fractional derivative supplemented with Stieltjes and generalized fractional integral boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a new generalized and sharp version of Jordan’s inequality which is a unified generalization of some known results. An application of our results to the improvement of the Yang Le inequality is provided in this paper. [Copyright &y& Elsevier]

In this paper, we establish the global well-posedness of mild solution to the three-dimensional incompressible generalized Navier–Stokes equations with Coriolis force if the initial data are in X 1 − 2 α defined by X 1 − 2 α = { u ∈ D ′ ( R 3 ) : ∫ R 3 | ξ | 1 − 2 α | u ˆ ( ξ ) | d ξ < + ∞ } . In addition, we also give Gevrey class regularity of the solution. [ABSTRACT FROM AUTHOR]

In this paper we establish a general decay rate for a quasilinear viscoelastic problem where the relaxation function satisfies g ′ ( t ) ≤ − ξ ( t ) g p ( t ) , t ≥ 0 , 1 ≤ p < 3 2 . This work generalizes and improves earlier results in the literature. [ABSTRACT FROM AUTHOR]

In this work we study aHammerstein generalized integral equation u ( t ) = ∫ − ∞ + ∞ k ( t , s ) f ( s , u ( s ) , u ′ ( s ) , … , u ( m ) ( s ) ) d s , where k : R 2 → R is a W m , ∞ ( R 2 ) , m ∈ N , kernel function and f : R m + 2 → R is a L 1 -Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence of a non-autonomous differential equation with a time-varying delay. The equation has important practical applications. It is shown that every solution of the equation is bounded and tends to a constant as t → + ∞ , which generalizes the Bernfeld–Haddock conjecture. Our result improves and extends some existing ones. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new modification of the half-linear Prüfer angle. Applying this modification, we investigate the conditional oscillation of the half-linear second order differential equation ( ∗ ) t α − 1 r ( t ) Φ ( x ′ ) ′ + t α − 1 − p s ( t ) Φ ( x ) = 0 , Φ ( x ) = | x | p − 1 sgn x , where p > 1 , α ≠ p , and r , s are continuous functions such that r ( t ) > 0 for large t . We present conditions on the functions r , s which guarantee that Eq. ( ∗ ) behaves like the Euler type equation [ t α − 1 Φ ( x ′ ) ] ′ + λ t α − 1 − p Φ ( x ) = 0 , which is conditionally oscillatory with the oscillation constant λ 0 = | p − α | p ∕ p p . [ABSTRACT FROM AUTHOR]

In this paper, the general equations of equilibrium for axisymmetrical deformation including the torsional deformation of shells with general forms are derived as stationary conditions of a generalized variational principle, which is established by the semi-inverse method. It shows that they are different from the results obtained by Chien (1990) in case of revolutional shell, therefore Chien’s results can be further improved. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following quasilinear Schrödinger equations: { − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) ∣ ∇ u ∣ 2 + V ( x ) u = K ( x ) f ( u ) , x ∈ R N , u ∈ D 1 , 2 ( R N ) , where N ≥ 3 and V , K are nonnegative continuous functions. Firstly by using a change of variables, the quasilinear equation is reduced to a semilinear one, whose associated functional is still not well defined in D 1 , 2 ( R N ) because of the potential vanishing at infinity. However, by using a Hardy-type inequality, we can work in the weighted Sobolev space in which the functional is well defined. Using this fact together with the variational methods, we obtain a positive solution. [ABSTRACT FROM AUTHOR]

In this paper, we give the existence of global L ∞ bounded entropy solutions for the Cauchy problem of a generalized n × n hyperbolic system of quadratic type. The main difficulty lies in establishing some compactness estimates of the viscosity solutions because the system has been generalized from 2 × 2 to n × n and some linearly degenerate characteristic fields emerged. We obtain the existence of the global weak solutions using the compensated compactness method coupled with the construction of entropy–entropy flux and BV estimates on viscosity solutions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized Hall-MHD system in dimension three. Global existence is investigated for 3D generalized Hall-MHD system provided that the initial data is small enough. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the Cauchy problem for the incompressible generalized magnetohydrodynamic equations in three space dimensions. By using the Lei and Lin (2011) argument in a slightly different fashion, we obtain the global existence of mild solutions, which enables us to prove analyticity of the solution. [ABSTRACT FROM AUTHOR]

This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P-splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials e α x , e − α x and linear functions multiplied by these exponentials, x e + α x and x e − α x . Here, we show that these types of penalized splines reproduce functions in the space { e − α x , x e − α x } , that is they fit exponential data exactly. Moreover, we show that they conserve the first and second 'exponential' moments. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of positive solutions to a second order boundary value problem. By imposing growth conditions on f and using a generalization of the Leggett–Williams fixed point theorem, we prove the existence of at least three symmetric positive solutions. [ABSTRACT FROM AUTHOR]

In this paper, the generalized shift-splitting preconditioner is implemented for saddle point problems with symmetric positive definite (1, 1)-block and symmetric positive semidefinite (2, 2)-block. The proposed preconditioner is extracted from a stationary iterative method which is unconditionally convergent. Moreover, a relaxed version of the proposed preconditioner is presented and some properties of the eigenvalues distribution of the corresponding preconditioned matrix are studied. Finally, some numerical experiments on test problems arisen from finite element discretization of the Stokes problem are given to show the effectiveness of the preconditioners. [ABSTRACT FROM AUTHOR]

In this paper, by using a novel approach, we first prove a new generalization of discrete-type Halanay inequality. Based on our new generalized inequality, a novel criterion for the exponential stability of a certain class of nonlinear non-autonomous difference equations is proposed. Numerical examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we consider the viscoelastic equation with a homogeneous Dirichlet condition on a portion of the boundary and acoustic boundary conditions on the rest of the boundary. By using the assumptions on the relaxation function due to Tatar (2011), we generalize the work of Park and Park (2011) to an arbitrary rate of decay with not necessarily of an exponential or polynomial one and without the assumption condition ∫ 0 ∞ g ( s ) d s < 1 2 . [ABSTRACT FROM AUTHOR]

In this paper, we consider multi-component generalizations of the Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation. By introducing a Lax pair, we present a matrix generalization of the Hirota-Satsuma coupled KdV equation, which is shown to be reduced to a vector Hirota-Satsuma coupled KdV equation. By using Hirota's bilinear method, we find a few soliton solutions to the vector Hirota-Satsuma coupled KdV equation in a symmetric case. Finally, in this symmetric case, we give a multi-soliton solution expressed by pfaffians and prove it by pfaffian techniques. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we generalize the inverse three spectra theorem for Sturm–Liouville problems. When the boundary problems on and subject two different boundary conditions at the midpoint , we show that under suitable circumstances, the potential and boundary conditions at endpoints are uniquely determined by the spectra of three boundary problems generated by the equation on the intervals , and , respectively. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the global regularity for the 2D generalized liquid crystal model with the fractional diffusion term for the velocity field and for the vector field modeling the orientation of the crystal molecules. Global existence of smooth solutions is proved for the case . [Copyright &y& Elsevier]

Abstract: In this paper, we prove the global regularity to the Cauchy problem of 3D incompressible magnetohydrodynamic- (MHD- ) model with fractional diffusion. We prove that if the exponents and satisfy with , then the 3D MHD- model with fractional diffusion admits a unique global smooth solution. [Copyright &y& Elsevier]

The constrained mock-Chebyshev least squares interpolation is a univariate polynomial interpolation technique exploited to cut-down the Runge phenomenon. It takes advantage of the optimality of the interpolation on the mock-Chebyshev nodes, i.e. the subset of the uniform grid formed by nodes that mimic the behavior of Chebyshev–Lobatto nodes. The other nodes of the grid are not discarded, rather they are used in a simultaneous regression to improve the accuracy of the approximation of the mock-Chebyshev subset interpolant. In this paper we extend the univariate constrained mock-Chebyshev least squares interpolation to the bivariate case in two different ways, relying on the tensor product interpolation and on the interpolation at the mock-Padua nodes. Numerical experiments demonstrate the effectiveness of such extensions. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the computation of the first probability density function of the solution of random homogeneous linear second-order difference equations by the Random Variable Transformation method. This approach allows us to generalize the classical solution obtained in the deterministic scenario. Several illustrative examples are provided. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to establish the continuity of the efficient solution mappings to a parametric generalized strong vector equilibrium problem, by using the Hölder relation. Our result extends and improves some recent results in the references therein. [Copyright &y& Elsevier]

Abstract: A number of papers intended for the numerical computation of generalized inverses by means of higher-order iterative methods have been published recently. This note investigates the numerical stability of a general family of iterative methods in order to complete the previous studies in this trend of research. [Copyright &y& Elsevier]

Abstract: In this paper, the lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems without the assumptions of monotonicity and compactness is established by using a new proof method which is different from the ones used in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, a generalized nonlinear dynamic integral inequality on time scales is established and then is used to study the boundedness of a class of nonlinear second-order dynamic equations on time scales. These theorems contain as special cases results for second-order differential equations, difference equations and -difference equations. [Copyright &y& Elsevier]

Abstract: In this paper, a -dimensional generalized Kadomtsev–Petviashvili (KP) equation is first discussed using the pfaffianization procedure. A -dimensional generalized coupled KP system is derived together with the Wronski-type pfaffian solution. Furthermore, the Gramm-type pfaffian solution for such a coupled system is presented and verified with the help of the pfaffian identities. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the generalized Hyers–Ulam stability of the Laplace’s equation, . [Copyright &y& Elsevier]

Abstract: In this paper, we consider a discrete fractional boundary value problem, for , of the form , , , where is continuous, , and . We prove that this problem can be interpreted as a discrete multipoint problem. We also show that the problem is a generalization of some recent results. Our results provide some basic analysis of discrete fractional boundary conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we show that the construction arising from a generalized topology and a hereditary class introduced by Á. Császár (2007) remains valid, together with many applications, if the generalized topology is replaced by a weak structure. [Copyright &y& Elsevier]

Abstract: In 2009, Ilić and Rakoc˘ević proved that quasi-contraction maps on normal cone metric spaces have a unique fixed point (Ilić and Rakoc˘ević, 2009 ). Then, Kadelburg, Radenović and Rakoc˘ević generalized their results by considering an additional assumption (Kadelburg et al., 2009 ). Also, they proved that quasi-contraction maps on cone metric spaces have the property (P) whenever . Later, Haghi, Rezapour and Shahzad proved same results without the additional assumption and for by providing a new technical proof (Rezapour et al., 2010 ). In 2011, Wardowski published a paper (Wardowski, 2011 ) and tried to test fixed point results for multifunctions on normal cone metric spaces. Of course, he used a special view in his results. Recently, Amini-Harandi proved a result on the existence of fixed points of set-valued quasi-contraction maps in metric spaces by using the technique of Rezapour et al. (2010) . But, like Kadelburg et al. (2009) , he could prove it only for (Amini-Harandi (2011) ). In this work, we prove again the main result of Amini-Harandi (2011) by using a simple method. Also, we introduce quasi-contraction type multifunctions and show that the main result of Amini-Harandi (2011) holds for quasi-contraction type multifunctions. [Copyright &y& Elsevier]

Abstract: In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz–Caputo derivative. First we prove a generalized Euler–Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the notion of a hybrid generalized multi-valued contraction mapping and establish the common fixed point theorem for this mapping. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature. [Copyright &y& Elsevier]

Abstract: The purpose of the present paper is to introduce two subclasses of -valent Bazilevic functions by using the generalized operator and to investigate various properties for these subclasses. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to introduce and investigate a new class of generalized Apostol–Bernoulli polynomials based on a definition given by Natalini and Bernardini (2003)  for the generalized Bernoulli polynomials. We obtain a generalization of the Srivastava–Pintér addition theorem (Srivastava and Pintér (2004) ). We also give a list of expressions involving special functions that could be used to obtain some analogues of the Srivastava–Pintér addition theorem. Finally, we give an analogue featuring the new class of generalized Apostol–Bernoulli polynomials. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of a set-valued contractive mapping is considered by using the idea of a generalized distance, such as the -distance, in metric spaces without using the concept of the Hausdorff metric. Furthermore, under some mild conditions, we provide the existence theorems for fixed-point problems of the considered mapping. Hence, our results can be viewed as a generalization and improvement of many recent results. [Copyright &y& Elsevier]

Abstract: In this paper we prove a Korovkin type approximation theorem and obtain the rate of convergence of the generalized Szász–Mirakjan–Beta operators by means of modulus of continuity and elements of Lipschitz class. Furthermore we give the -statistical approximation theorem for these operators and investigate the case which provides the best estimation. [Copyright &y& Elsevier]

Abstract: In this paper, a new Picone-type identity for the quasilinear differential operator of the second order is used to establish an integral inequality involving functions and their derivatives which generalizes the classical Wirtinger inequality. [Copyright &y& Elsevier]

Abstract: In this paper we obtain some applications of first order differential subordination and superordination results involving generalized Sălăgean integral operator for certain normalized analytic functions. Some of our results generalize previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we prove a generalization of Aczél’s inequality. The obtained inequalities extend some results established recently. We also give some comments on a recent result concerning the refinements of the generalized Aczél–Popoviciu’s inequality. [Copyright &y& Elsevier]

Abstract: The competition graph of a doubly partial order is an interval graph. The competition-common enemy graph, a variant of the competition graph, of a doubly partial order is also an interval graph if it does not contain a 4-cycle as an induced subgraph. It is natural to ask whether or not the same phenomenon occurs for other interesting variants of the competition graph. In this paper, we study the -step competition graph, a generalization of the competition graph, of a doubly partial order. We show that the -step competition graph of a doubly partial order is an interval graph for every positive integer . We also show that given a positive integer , an interval graph with sufficiently many isolated vertices is the -step competition graph of a doubly partial order. [Copyright &y& Elsevier]

Abstract: This paper deals with a new generalization of the Garfunkel–Bankoff inequality by introducing a parameter, which relaxes the conditions of the Garfunkel–Bankoff inequality. As applications, an improved version of the Finsler–Hadwiger inequality is obtained. [Copyright &y& Elsevier]