# Journal of Inequalities and Applications

http://www.journalofinequalitiesandapplications.com/

## List of Papers (Total 3,411)

#### An algorithm for the split-feasibility problems with application to the split-equality problem

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

#### Two variables functionals and inequalities related to measurable operators

In this paper, we introduce two variables norm functionals of τ-measurable operators and establish their joint log-convexity. Applications of this log-convexity will include interpolated Young, Heinz and Trace inequalities related to τ-measurable operators. Additionally, interpolated versions and their monotonicity will be presented as well.

#### New applications of Schrödinger type inequalities in the Schrödingerean Hardy space

As new applications of Schrödinger type inequalities obtained by Jiang (J. Inequal. Appl. 2016: Article ID 247, 2016) in the Schrödingerean Hardy space, we not only obtain the representation of Schrödingerean harmonic functions but also give a sufficient and necessary condition between the Schrödingerean distributional function and its derivative in the Schrödingerean Hardy space.

#### An algorithm for the split-feasibility problems with application to the split-equality problem

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

#### On a boundary property of analytic functions

Let f be an analytic function in the unit disc | z | < 1 $|z|<1$ on the complex plane C $\mathbb {C}$ . This paper is devoted to obtaining the correspondence between f ( z ) $f(z)$ and z f ′ ( z ) $zf'(z)$ at the point w, 0 < | w | = R < 1 $0<|w|=R< 1$ , such that | f ( w ) | = min { | f ( z ) | : f ( z ) ∈ ∂ f ( | z | ≤ R ) } $|f(w)|=\min \{|f(z)|: f(z)\in\partial f(|z|\leq R) \}$ ...

#### Degenerate Changhee-Genocchi numbers and polynomials

In this paper, we study some properties of degenerate Changhee-Genocchi numbers and polynomials and give some new identities of these polynomials and numbers which are derived from the generating function. In particular, we provide interesting identities related to the Changhee-Genocchi polynomials of the second kind and Changhee-Genocchi numbers of the second kind.

#### A class of retarded Volterra-Fredholm type integral inequalities on time scales and their applications

In this paper, we study some new retarded Volterra-Fredholm type integral inequalities on time scales, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as tools in the qualitative theory of certain classes of retarded dynamic equations on time scales. Some applications are also presented to ...

#### Degenerate Changhee-Genocchi numbers and polynomials

In this paper, we study some properties of degenerate Changhee-Genocchi numbers and polynomials and give some new identities of these polynomials and numbers which are derived from the generating function. In particular, we provide interesting identities related to the Changhee-Genocchi polynomials of the second kind and Changhee-Genocchi numbers of the second kind.

#### A class of retarded Volterra-Fredholm type integral inequalities on time scales and their applications

In this paper, we study some new retarded Volterra-Fredholm type integral inequalities on time scales, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as tools in the qualitative theory of certain classes of retarded dynamic equations on time scales. Some applications are also presented to ...

#### On a boundary property of analytic functions

Let f be an analytic function in the unit disc | z | < 1 $|z|<1$ on the complex plane C $\mathbb {C}$ . This paper is devoted to obtaining the correspondence between f ( z ) $f(z)$ and z f ′ ( z ) $zf'(z)$ at the point w, 0 < | w | = R < 1 $0<|w|=R< 1$ , such that | f ( w ) | = min { | f ( z ) | : f ( z ) ∈ ∂ f ( | z | ≤ R ) } $|f(w)|=\min \{|f(z)|: f(z)\in\partial f(|z|\leq R) \}$ ...

#### A class of retarded Volterra-Fredholm type integral inequalities on time scales and their applications

In this paper, we study some new retarded Volterra-Fredholm type integral inequalities on time scales, which provide explicit bounds on unknown functions. These inequalities generalize and extend some known inequalities and can be used as tools in the qualitative theory of certain classes of retarded dynamic equations on time scales. Some applications are also presented to ...

#### Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

This paper is concerned with an explicit value of the embedding constant from W 1 , q ( Ω ) $W^{1,q}(\Omega)$ to L p ( Ω ) $L^{p}(\Omega)$ for a domain Ω ⊂ R N $\Omega\subset\mathbb{R}^{N}$ ( N ∈ N $N\in\mathbb{N}$ ), where 1 ≤ q ≤ p ≤ ∞ $1\leq q\leq p\leq\infty$ . We previously proposed a formula for estimating the embedding constant on bounded and unbounded Lipschitz domains by ...

#### A weighted denoising method based on Bregman iterative regularization and gradient projection algorithms

A weighted Bregman-Gradient Projection denoising method, based on the Bregman iterative regularization (BIR) method and Chambolle’s Gradient Projection method (or dual denoising method) is established. Some applications to image denoising on a 1-dimensional curve, 2-dimensional gray image and 3-dimensional color image are presented. Compared with the main results of the ...

#### Monotonicity, convexity, and inequalities for the generalized elliptic integrals

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals K a ( r ) $\mathscr{K}_{a}(r)$ and E a ( r ) $\mathscr {E}_{a}(r)$ depending on a parameter a ∈ ( 0 , 1 ) $a\in(0,1)$ , which contains an earlier result in the particular case a = 1 / 2 $a=1/2$ .

#### New results on reachable set bounding for linear time delay systems with polytopic uncertainties via novel inequalities

This work is further focused on analyzing a bound for a reachable set of linear uncertain systems with polytopic parameters. By means of L-K functional theory and novel inequalities, some new conditions which are expressed in the form of LMIs are derived. It should be noted that novel inequalities can improve upper bounds of Jensen inequalities, which yields less conservatism of ...

#### Chebyshev type inequalities by means of copulas

A copula is a function which joins (or ‘couples’) a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

#### New results on the continuous Weinstein wavelet transform

We consider the continuous wavelet transform S h W $\mathcal{S}_{h}^{W}$ associated with the Weinstein operator. We introduce the notion of localization operators for S h W $\mathcal {S}_{h}^{W}$ . In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of S h W ...

#### Nonexistence of global solutions of abstract wave equations with high energies

We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are ...

#### Janowski type close-to-convex functions associated with conic regions

The analytic functions, mapping the open unit disk onto petal and oval type regions, introduced by Noor and Malik (Comput. Math. Appl. 62:2209-2217, 2011), are considered to define and study their associated close-to-convex functions. This work includes certain geometric properties like sufficiency criteria, coefficient estimates, arc length, the growth rate of coefficients of ...

#### A novel finite-time average consensus protocol based on event-triggered nonlinear control strategy for multiagent systems

We present a novel finite-time average consensus protocol based on event-triggered control strategy for multiagent systems. The system stability is proved. The lower bound of the interevent time is obtained to guarantee that there is no Zeno behavior. Moreover, the upper bound of the convergence time is obtained. The relationship between the convergence time and protocol parameter ...

#### Inequalities and asymptotics for some moment integrals

For α > β − 1 > 0 $\alpha>\beta-1>0$ , we obtain two-sided inequalities for the moment integral I ( α , β ) = ∫ R | x | − β | sin x | α d x $I(\alpha,\beta)=\int_{\mathbb{R}}|x|^{-\beta}|\sin x|^{\alpha}\,dx$ . These are then used to give the exact asymptotic behavior of the integral as α → ∞ $\alpha\rightarrow\infty$ . The case I ( α , α ) $I(\alpha,\alpha)$ corresponds to the ...