Journal of Inequalities and Applications最新文献

Some new nonlinear impulsive differential and integral inequalities with nonlocal integral jump conditions are presented in this paper. Using the method of mathematical induction, we obtain a new upper bound estimation of certain differential and integral inequalities; these inequalities have both nonlocal integral jump and weakly singular kernels. Finally, we give two examples of these inequalities in estimating solutions of certain equations with Riemann-Liouville fractional integral conditions.

In this paper, we deal with the problem of finding the best possible bounds for the first Seiffert mean in terms of the geometric combination of logarithmic and the Neuman-Sándor means, and in terms of the geometric combination of logarithmic and the second Seiffert means.

In this paper, we investigate the existence of common fixed points of a certain mapping in the frame of an extended b-metric space. The given results cover a number of well-known fixed point theorems in the literature. We state some examples to illustrate our results.

Let $r\ge 1$ , $1\le p<2$ , and $\alpha ,\beta >0$ with $1/\alpha +1/\beta =1/p$ . Let $\{a_{nk},1\le k\le n,n\ge 1\}$ be an array of constants satisfying ${sup}_{n\ge 1}{n}^{-1}{\sum }_{k=1}^n{\left|a_{nk}\right|}^{\alpha }<\infty$ , and let $\{X_n,n\ge 1\}$ be a sequence of identically distributed ${\rho }^{\ast }$ -mixing random variables. For each of the three cases $\alpha <rp$ , $\alpha =rp$ , and $\alpha >rp$ , we provide moment conditions under which $\sum _{n=1}^{\infty }{n}^{r-2}P\left\{\underset{1\le m\le n}{max}\right|\sum _{k=1}^m{a}_{nk}{X}_k|>\epsilon n^{1/p}\}<\infty ,\forall \epsilon >0.$ We also provide moment conditions under which $\sum _{n=1}^{\infty }{n}^{r-2-q/p}E{\left(\underset{1\le m\le n}{max}\right|\sum _{k=1}^m{a}_{nk}{X}_k|-\epsilon n^{1/p})}_{+}^q<\infty ,\forall \epsilon >0,$ where $q>0$ . Our results improve and generalize those of Sung (Discrete Dyn

We solve an open problem on some majorization inequalities involving the cyclic moving average.

Let $T_{\Pi \overrightarrow{b}}$ be the commutator generated by a multilinear square function and Lipschitz functions with kernel satisfying Dini-type condition. We show that $T_{\Pi \overrightarrow{b}}$ is bounded from product Lebesgue spaces into Lebesgue spaces, Lipschitz spaces, and Triebel-Lizorkin spaces.

Recently, Kittaneh and Manasrah (J. Math. Anal. Appl. 361:262-269, 2010) showed a refinement of the arithmetic-geometric mean inequality for the Frobenius norm. In this paper, we shall present a generalization of Kittaneh and Manasrah's result. Meanwhile, we will also give an application of Kittaneh and Manasrah's result. That is, we obtain an improvement of Jocić and Kittaneh's inequality which was presented in (Jocić and Kittaneh in J. Oper. Theory 31:3-10, 1994).

We state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order $\alpha \in (1,2]$ with mixed non-linearities of the form $\left(T_{\alpha }^{a}x\right)\left(t\right)+r_1\left(t\right)\left|x\right(t\left){|}^{\eta -1}x\right(t)+r_2(t\left)\right|x\left(t\right){|}^{\delta -1}x\left(t\right)=g\left(t\right),t\in (a,b),$ satisfying the Dirichlet boundary conditions $x\left(a\right)=x\left(b\right)=0$ , where $r_1$ , $r_2$ , and g are real-valued integrable functions, and the non-linearities satisfy the conditions $0<\eta <1<\delta <2$ . Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative $T_{\alpha }^a$ is replaced by a sequential conformable derivative $T_{\alpha }^a\circ T_{\alpha }^a$ , $\alpha \in (1/2,1]$ . The potential functions $r_1$ , $r_2$ as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.

In this paper, we present some identities relating the hyperharmonic, the Daehee and the derangement numbers, and we derive some nonlinear differential equations from the generating function of a hyperharmonic number. In addition, we use this differential equation to obtain some identities in which the hyperharmonic numbers and the Daehee numbers are involved.

This paper focuses on a class of nonlinear optimization subject to linear inequality constraints with unavailable-derivative objective functions. We propose a derivative-free trust-region methods with interior backtracking technique for this optimization. The proposed algorithm has four properties. Firstly, the derivative-free strategy is applied to reduce the algorithm's requirement for first- or second-order derivatives information. Secondly, an interior backtracking technique ensures not only to reduce the number of iterations for solving trust-region subproblem but also the global convergence to standard stationary points. Thirdly, the local convergence rate is analyzed under some reasonable assumptions. Finally, numerical experiments demonstrate that the new algorithm is effective.