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 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 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 iterative methods for solving nonlinear equations by using modified homotopy perturbation method.
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.
New retarded integral inequalities with applications.
New strengthened Carleman's inequality and Hardy's inequality.
New upper and lower bounds for the Čebyšev functional.
New upper bounds for Mathieu-type series.
New variants of Khintchine's inequality.
Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.