Journal of Inequalities and Applications

http://www.journalofinequalitiesandapplications.com/

List of Papers (Total 3,394)

An inequality for generalized complete elliptic integral

In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.

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 inequality for generalized complete elliptic integral

In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.

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.

A new look at classical inequalities involving Banach lattice norms

Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by...

An inequality for generalized complete elliptic integral

In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.

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.

A new look at classical inequalities involving Banach lattice norms

Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by...

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...

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...

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.

Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

In this paper, we propose and analyze a hybrid iterative method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inequality problem, and the set of fixed points of a relatively nonexpansive mapping in a real Banach space. Further, we prove the strong convergence of the sequences generated by the...

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...

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.