In this paper, a class of nonlinear constrained optimization problems with both inequality and equality constraints is discussed. Based on a simple and effective penalty parameter and the idea of primal-dual interior point methods, a QP-free algorithm for solving the discussed problems is presented. At each iteration, the algorithm needs to solve two or three reduced systems of...

In this paper, we consider the numerical solution for the discretization of semilinear elliptic complementarity problems. A monotone algorithm is established based on the upper and lower solutions of the problem. It is proved that iterates, generated by the algorithm, are a pair of upper and lower solution iterates and converge monotonically from above and below, respectively, to...

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying...

In this paper, a new form of the symmetric vector equilibrium problem is introduced and, by mixing properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for it is established. We show that Ky Fan’s lemma, as a usual technique for proving the existence results for equilibrium problems, implies the maximal element lemma, while it is...

In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of R d $\mathbb{R}^{d}$ with smooth boundary ∂Ω. Our result shows that the value of the solutions can be determined uniquely by its value on an arbitrary open subset ω of Ω at any given positive time T.

We construct sequences of finite sums ( l ˜ n ) n ≥ 0 $(\tilde{l}_{n})_{n\geq 0}$ and ( u ˜ n ) n ≥ 0 $(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product...

In this article, two types of Hardy’s inequalities for the twisted convolution with Laguerre functions are studied. The proofs are mainly based on an estimate for the Heisenberg left-invariant vectors of the special Hermite functions deduced by the Heisenberg group approach.

In the present study, we work on the problem of the existence of positive solutions of fractional integral equations by means of measures of noncompactness in association with Darbo’s fixed point theorem. To achieve the goal, we first establish new fixed point theorems using a new contractive condition of the measure of noncompactness in Banach spaces. By doing this we generalize...

In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is ( k + 3 / 2 ) $(k+3/2)$ th-order superconvergent to a particular projection of the exact solution, when the upwind flux and the alternating fluxes are used. The proof is valid for arbitrary nonuniform...

A class of 4-band symmetric biorthogonal wavelet bases has been constructed, in which any wavelet system the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters. Thus, the least restrictive conditions are needed for forming a wavelet so that the free degrees can be reversed for application requirement. Some concrete...

The present study considers the robust stability for impulsive complex-valued neural networks (CVNNs) with discrete time delays. By applying the homeomorphic mapping theorem and some inequalities in a complex domain, some sufficient conditions are obtained to prove the existence and uniqueness of the equilibrium for the CVNNs. By constructing appropriate Lyapunov-Krasovskii...

Most mathematical models arising in stationary filtration processes as well as in the theory of soft shells can be described by single-valued or generalized multivalued pseudomonotone mixed variational inequalities with proper convex nondifferentiable functionals. Therefore, for finding the minimum norm solution of such inequalities, the current paper attempts to introduce a...

In this study, we first present a classical finite element (FE) method for a two-dimensional (2D) viscoelastic wave equation and analyze the existence, stability, and convergence of the FE solutions. Then we establish an optimized FE extrapolating (OFEE) method based on a proper orthogonal decomposition (POD) method for the 2D viscoelastic wave equation and analyze the existence...

In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term. The main tools adopted in our proofs are the concentration compactness principle and Nehari manifold.

Given a sequence { f n } n ∈ N of measurable functions on a σ-finite measure space such that the integral of each f n as well as that of lim sup n ↑ ∞ f n exists in R ‾ , we provide a sufficient condition for the following inequality to hold: lim sup n ↑ ∞ ∫ f n d μ ≤ ∫ lim sup n ↑ ∞ f n d μ . Our condition is considerably weaker than sufficient conditions known in the literature...

In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: u ( s ) = ϕ i ( s ) + ∫ a b K i ( s , r , u ( r ) ) d r , where s ∈ ( a , b ) ⊆ R ; u , ϕ i ∈ C ( ( a , b ) , R n ) and K i : ( a , b...

We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring’s lemma, we prove that these very weak solutions are weak solutions. Further, we show that these solutions are in fact...

We establish necessary and sufficient conditions for the one-dimensional differential Hardy inequality to hold, including the overdetermined case. The solution is given in terms different from those of the known results. Moreover, the least constant for this inequality is estimated. MSC: 26D10, 47B38.

In this paper a method for studying stability of the equation x ″ ( t ) + ∑ i = 1 m a i ( t ) x ( t − τ i ( t ) ) = 0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x ″ ( t ) + ∑ i = 1 m a i ( t ) x ( t ) = 0 is not exponentially stable, the delay equation can be exponentially stable. MSC...

We obtain refined estimates of the triangle inequality in a normed space using integrals and the Tapia semi-product. The particular case of an inner product space is discussed in more detail. MSC: 46B99, 26D15, 46C50, 46C05.

In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type inequality are shown. MSC: 26D10, 26D15.

In this paper, the idea of lacunary I λ -statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary I λ -statistical convergence with lacunary I λ -summable sequences. Moreover, we study the I λ -lacunary statistical convergence in probabilistic normed space and discuss some topological properties.

In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate...

Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Assume that g is a real-valued convex function and the gradient ∇g is 1 L -ism with L > 0 . Let 0 < λ < 2 L + 2 , 0 < β n < 1 . We prove that the sequence { x n } generated by the iterative algorithm x n + 1 = P C ( I − λ ( ∇ g + β n I ) ) x n , ∀ n ≥ 0 converges strongly to q ∈ U , where q = P U ( 0...