We give a short and elementary proof of an inverse Bernsteintype inequality found by S. Khrushchev for the derivative of a polynomial having all its zeros on the unit circle . The inequality is used to show that equally-spaced points solve a min-max-min problem for the logarithmic potential of such polynomials. Using techniques recently developed for polarization (Chebyshev-type) problems, we s...

In this   paper,  we   present  some  refinements  of the   famous Young  type  inequality.   As  application  of   our   result, we  obtain  some  matrix inequalities   for   the  Hilbert-Schmidt norm  and   the  trace   norm. The results    obtained   in  this  paper  can  be   viewed   as  refinement  of  the   derived  results   by  H.  Kai  [Young  type  inequalities  for matrices,  J.  Ea...

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...

The inverse tangent function can be bounded by different inequalities, for example by Shafer’s inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent function. In particular, we sharpen Shafer’s inequality and calculate the best corresponding constants. The maximum relative errors of the obtained bounds are ap...

In the past six decades, lifespan inequality has varied greatly within and among countries even while life expectancy has continued to increase. How and why does mortality change generate this diversity? We derive a precise link between changes in age-specific mortality and lifespan inequality, measured as the variance of age at death. Key to this relationship is a young-old threshold age, belo...