Let G be a simple connected graph and S 2 ( G ) be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) among all bicyclic graphs of order n, which confirms the conjecture of Guan et al. (J. Inequal. Appl. 2014:242, 2014 ) for the case of bicyclic graphs. MSC: 05C50, 15A48.

We know that variational inequality problem is very important in the nonlinear analysis. The main purpose of this paper is to propose an iterative method for finding an element of the set of solutions of a variational inequality problem with a monotone and Lipschitz continuous mapping in Hilbert space. This iterative method is based on the extragradient method. We get a weak ...

In mathematical chemistry, the median eigenvalues of the adjacency matrix of a molecular graph are strictly related to orbital energies and molecular orbitals. In this regard, the difference between the occupied orbital of highest energy (HOMO) and the unoccupied orbital of lowest energy (LUMO) has been investigated (see Fowler and Pisansky in Acta Chim. Slov. 57:513-517, 2010 ). ...

In the setting of the Heisenberg group H n , we characterize those nonnegative functions w defined on [ 0 , 1 ] for which the weighted Hardy operator H w is bounded on L p ( H n ) , 1 ≤ p ≤ ∞ , and on BMO ( H n ) . Meanwhile, the corresponding operator norm in each case is derived. Furthermore, we introduce a type of weighted multilinear Hardy operators and obtain the ...

In this paper, we propose several new iterative algorithms to solve the split feasibility problem in the Hilbert spaces. By virtue of new analytical techniques, we prove that the iterative sequence generated by these iterative procedures converges to the solution of the split feasibility problem which is the best close to a given point. In particular, the minimum-norm solution can ...

In this short note, we present some trace inequalities for matrix means. Our results are generalizations of the ones shown by Bhatia, Lim, and Yamazaki. MSC: 47A63.

In this article, a functional minimum problem equivalent to the p-Laplace equation is introduced, a finite element-Newton iteration formula is established, and a well-posed condition of iterative functions satisfied is provided. According to the well-posed condition, an effective initial iterative function is presented. Using the effective particular initial function and Newton ...

In this paper, we present an optimization technique to find the optimal parameters of the AOR iteration, which just needs to minimize the 2-norm of the residual vector and avoids solving the spectral radius of the iteration matrix of the SOR method. Meanwhile, numerical results are provided to indicate that the new method is more robust than the AOR method for larger intervals of ...

This paper gives a new theoretical analysis of the space-time continuous Galerkin (STCG) method for the wave equation. We prove the existence and uniqueness of the numerical solutions and get optimal orders of convergence to numerical solutions regarding space that do not need any compatibility conditions on the space and time mesh size. Finally, we employ a numerical example to ...

Let U n denote the nth Cohen number. Some combinatorial properties for U n have been discovered. In this paper, we prove the ratio log-concavity of U n by establishing the lower and upper bounds for U n U n − 1 . MSC: 05A20, 11B83.

In this paper, we provide Lagrange-type duality theorems for mathematical programming problems with DC objective and constraint functions. The class of problems to which Lagrange-type duality theorems can be applied is broader than the class in the previous research. The main idea is to consider equivalent inequality systems given by the maximization of the original functions. In ...

In this paper, the boundedness in Lebesgue spaces for multilinear fractional integral operators and commutators generated by multilinear fractional integrals with an RBMO ( μ ) function on non-homogeneous metric measure spaces is obtained. MSC: 42B25, 47B47.

In this paper, we first show that the first Seiffert mean P is concave whereas the second Seiffert mean T and the Neuman-Sándor mean NS are convex. As applications, we establish the sub-stabilizability/super-stabilizability of certain bivariate means. Open problems are derived as well. MSC: 26E60.

In this note, we try to generalize the classical Cauchy-Lipschitz-Picard theorem on the global existence and uniqueness for the Cauchy initial value problem of the ordinary differential equation with global Lipschitz condition, and we try to weaken the global Lipschitz condition. We can also get the global existence and uniqueness. MSC: 34A34, 34C25, 34C37.

In this paper, we study the log-behavior of a new sequence { S n } n = 0 ∞ , which was defined by Z-W Sun. We find that the sequence is log-convex by using the interlacing method. Additionally, we consider ratio log-behavior of { S n } n = 0 ∞ and find the sequences { S n + 1 / S n } n = 0 ∞ and { S n n } n = 1 ∞ are log-concave. Our results give an affirmative answer to a ...

We present some refinements of the Cauchy-Schwarz and Heinz inequalities for operators by utilizing a refinement of the Hermite-Hadamard inequality. MSC: 15A45, 15A60.

Let q > 2 be an integer, n ⩾ 2 be a fixed integer with ( n , q ) = 1 , ψ be a non-principal Dirichlet character modq. An upper bound estimate for character sums of the form ∑ a ∈ C ( 1 , q ) ψ ( a ) is given, where C ( 1 , q ) = { a ∣ 1 ⩽ a ⩽ q − 1 , a a ‾ ≡ 1 ( mod q ) , n ∤ ( a + a ‾ ) } . MSC: 11L05, 11L40, 11N37.

In this paper, we give new conditions under which the Cîrtoaje’s conjecture is also valid. We also show that a certain generalization of the Cîrtoaje’s inequality fulfils an interesting property. MSC: 26D10, 26D15.

Two new lower bounds for the minimum eigenvalue of an irreducible M-tensor are given. It is proved that the new lower bounds improve the corresponding bounds obtained by He and Huang (J. Inequal. Appl. 2014:114, 2014 ). Numerical examples are given to verify the theoretical results. MSC: 15A18, 15A69, 65F10, 65F15.

The new sequence spaces X ( r , s , t ; Δ ) for X ∈ { l ∞ , c , c 0 } have been defined by using generalized means and difference operator. In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on some new difference sequence spaces X ( r , s , t ; Δ ) where X ∈ { l ∞ , c , c 0 , l p } ( 1 ≤ ...

This paper is devoted to the study of optimality conditions for strict minimizers of higher-order for a non-smooth semi-infinite multi-objective optimization problem. We propose a generalized Guignard constraint qualification and a generalized Abadie constraint qualification for this problem under which necessary optimality conditions are proved. Under the assumptions of ...

In this note, we generalize some determinantal inequalities which are due to Lynn (Proc. Camb. Philos. 60:425-431, 1964 ), Chen (Linear Algebra Appl. 368:99-106, 2003 ) and Ando (Linear Multilinear Algebra 8:291-316, 1980 ). MSC: 47A63, 47A30.

In the paper, we establish a Lyapunov inequality and two Lyapunov-type inequalities for a higher-order fractional boundary value problem with a controllable nonlinear term. Two applications are discussed. One concerns an eigenvalue problem, the other a Mittag-Leffler function. MSC: 26A33, 26D10, 33E12, 34A08.

The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integral M β , ρ , q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel satisfies a certain Hörmander-type condition, the authors prove that M β , ρ , q is bounded from Lebesgue space L ...

In this paper, based on the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method, the nonlinear MHSS-like iteration method is presented to solve a class of the weakly absolute value equations (AVE). By using a smoothing approximate function, the convergence properties of the nonlinear MHSS-like iteration method are presented. Numerical experiments are reported to ...