Necessary and sufficient conditions for joint lower and upper estimates.
Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I.
Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. II.
New bounds for weights.
New bounds for the identric mean of two arguments.
New Čebyšev type inequalities via trapezoidal-like rules.
New equivalent conditions for Hardy-type inequalities
We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial in the study of oscillation and non-oscillation properties of differential equation solutions, as well as spectral properties.
New inequalities between elementary symmetric polynomials.
New inequalities involving the zeta function.
New inequalities obtained by means of quadrature formulae.
New inequalities of Hadamard's type for Lipschitzian mappings.
New inequalities of Shafer-Fink type for arc hyperbolic sine.
New inequalities similar to Hardy-Hilbert inequality and their applications.
New integral inequalities for iterated integrals with applications.
New iterative methods for solving nonlinear equations by using modified homotopy perturbation method.
New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights
We obtain Hardy type inequalities and their Orlicz-norm counterparts with an N-function M, power, power-logarithmic and power-exponential weights ω, ρ, holding on suitable dilation invariant supersets of C 0∞(ℝ+). Maximal sets of admissible functions u are described. This paper is based on authors’ earlier abstract results and applies them to particular classes of weights.
New Ostrowski type inequalities involving the product of two functions.
New Ostrowski type inequalities via mean value theorems.
New results in discrete asymptotic analysis.
New results in extremal problems with polynomials.