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## Refinements of Hardy-Type Inequalities on Time Scales | Mathematical Research Publishers

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Some features of this site may not work without it. My Account Login Register. Help How to submit and FAQs. Show simple item record New hilbert dynamic inequalities on time scales dc. Document information Title:. A new discrete Hardy-type inequality with kernels and monotone functions. Journal of Inequalities and Applications. Table of contents — Volume , Issue 1 Show all volumes and issues Tables of content are generated automatically and are based on records of articles contained that are available in the TIB-Portal index.

Iterative methods for split variational inclusion and fixed point problem of nonexpansive semigroup in Hilbert spaces. An algorithm with strong convergence for the split common fixed point problem of total asymptotically strict pseudocontraction mappings. Multi-parameter fourth order impulsive integral boundary value problems with one-dimensional m-Laplacian and deviating arguments.

Iterative methods for solving a class of monotone variational inequality problems with applications. A generalization of almost sure local limit theorem of uniform empirical process. Scalarized system of nonsmooth vector quasi-variational inequalities with applications to Debreu type vector equilibrium problems. A customized proximal point algorithm for stable principal component pursuit with nonnegative constraint.

A solution for the non-cooperative equilibrium problem of two person via fixed point theory. Critical curves for fast diffusion equations coupled via nonlinear boundary flux. On interval-valued invex mappings and optimality conditions for interval-valued optimization problems. Complete moment convergence for product sums of sequence of extended negatively dependent random variables.

The regularized trace formula for a fourth order differential operator given in a finite interval. A Hilbert-type integral inequality in the whole plane with a non-homogeneous kernel and a few parameters. The improved results in almost sure central limit theorem for the maxima of strongly dependent stationary Gaussian vector sequences. Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problems. Convexity and concavity of the complete elliptic integrals with respect to Lehmer mean.

Split hierarchical variational inequality problems and fixed point problems for nonexpansive mappings. Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process. Two spectral gradient projection methods for constrained equations and their linear convergence rate. Iterative methods for triple hierarchical variational inequalities with mixed equilibrium problems, variational inclusions, and variational inequalities constraints.

Some relationships among the constraint qualifications for Lagrangian dualities in DC infinite optimization problems. A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces. Limit properties of exceedance point processes of strongly dependent normal sequences. On function spaces with fractional Fourier transform in weighted Lebesgue spaces.

Bidimensional discrete-time risk models based on bivariate claim count time series. Blow-up solutions to the Cauchy problem of a fractional reaction-diffusion system. On pth moment exponential stability of stochastic differential equations with Markovian switching and time-varying delay.

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Symmetric duality for a higher-order nondifferentiable multiobjective programming problem. On refined Hardy-Knopp type inequalities in Orlicz spaces and some related results. An explicit version of the Chebyshev-Markov-Stieltjes inequalities and its applications. Hybrid iterative algorithm for finite families of countable Bregman quasi-Lipschitz mappings with applications in Banach spaces.

Empirical likelihood-based inference in Poisson autoregressive model with conditional moment restrictions. Some sufficient efficiency conditions in semiinfinite multiobjective fractional programming based on exponential type invexities. Oscillations of even order half-linear impulsive delay differential equations with damping. A general theorem on the stability of a class of functional equations including monomial equations. A modified regularization method for finding zeros of monotone operators in Hilbert spaces. Sufficiency and duality in nondifferentiable multiobjective programming involving higher order strong invexity.

The existence and uniqueness of the solution for nonlinear elliptic equations in Hilbert spaces. On a composition of two Hilbert-Hardy-type integral operators and related inequalities. Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square II. On the Ulam type stability of several types of quadratic fuzzy set-valued functional equations. A new class of analytic functions defined by means of a generalization of the Srivastava-Attiya operator. Some estimates of intrinsic square functions on the weighted Herz-type Hardy spaces.

A general uniqueness theorem concerning the stability of monomial functional equations in fuzzy spaces. Some new estimations for the upper and lower bounds for the spectral radius of nonnegative matrices. Some inequalities for the minimum eigenvalue of the Hadamard product of an M-matrix and an inverse M-matrix. Regularization and stability estimates for an inverse source problem of the radially symmetric parabolic equation. Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator.

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On the meromorphic solutions of certain class of nonlinear differential equations. A hybrid iterative method for a common solution of variational inequalities, generalized mixed equilibrium problems, and hierarchical fixed point problems. Monotonicity properties of a function involving the psi function with applications. Strong convergence theorems for fixed point problems, variational inequality problems, and equilibrium problems. A posteriori error estimates of mixed finite element solutions for fourth order parabolic control problems.

On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously. Estimates of the modular-type operator norm of the general geometric mean operator.

Optimality and duality results for a nondifferentiable multiobjective fractional programming problem. Statistical inference for first-order random coefficient integer-valued autoregressive processes. Nonconforming double set parameter finite element methods for a fourth order variational inequality with two-sided displacement obstacle. Imbedding inequalities for the composite operator in the Sobolev spaces of differential forms. Lipschitz and BMO norm inequalities for the composite operator on differential forms. For the development of the use of convexity argument in obtaining Hardy-type inequalities, we refer interested readers to the review article by Oguntuase and Persson [ 9 ] and the references cited therein.

In a recent paper, Oguntuase et al.

## Extensions of Holder-type inequalities on time scales and their applications

In particular, the following result was established. Observe that under suitable substitutions, all the variants 1. Thus 1. It is a great interest of this subject see, e. Before we present our results, let us recall some essentials about time scales. In , Hilger introduced the calculus on time scales which unifies continuous and discrete analysis. Note that we have. For more understanding of the theory of time scales, we refer the interested reader to [ 25 , 26 ].

Then the following estimates hold :. Thus we get. The techniques for doing this can be found in the papers [ 20 — 24 ] and the details are left to interested readers.

Therefore the two inequalities above hold in the reverse direction so also this case is proved. This inequality is very useful in the proof of our results in this section. For the proof, see [ 16 ]. The proof is now complete. The sign of inequality 3. Inequality 3. Under these conditions, inequality 3. Then inequality 3.