Some inverse mapping theorems
Some Kurzweil-Henstock-type integrals and the wide Denjoy integral
Kurzweil-Henstock integrals related to local systems and the wide Denjoy integral are discussed in the frame of their comparability and compatibility.
Some Landau's type inequalities for infinitesimal generators.
Some localization theorems using a majorization technique.
Some matrix inequalities of London type
Some mean value theorems as consequences of the Darboux property
The aim of the paper is to present some mean value theorems obtained as consequences of the intermediate value property. First, we will prove that any nonextremum value of a Darboux function can be represented as an arithmetic, geometric or harmonic mean of some different values of this function. Then, we will present some extensions of the Cauchy or Lagrange Theorem in classical or integral form. Also, we include similar results involving divided differences. The paper was motivated by some problems...
Some Mean-Value Theorems of the Cauchy Type
2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05Some mean-value theorems of the Cauchy type, which are connected with Jensen’s inequality, are given in [2] in discrete form and in [5] in integral form. Several further generalizations and applications of these results are presented here.
Some monotonicity results for the ratio of two-parameter symmetric homogeneous functions.
Some multiplicative inequalities for inner products and of the Carlson type.
Some new bounds for Mathieu's series.
Some new discrete inequalities and their applications.
Some new discrete nonlinear delay inequalities and application to discrete delay equations.
Some new generalizations of Hardy's integral inequality.
Some new Hardy type inequalities and their limiting inequalities.
Some new Hilbert-Pachpatte's inequalities.
Some new Hilbert's type inequalities.
Some new inequalities for gamma and polygamma functions.
Some new inequalities for means of two arguments.
Some new inequalities for the gamma, beta and zeta functions.
Some new inequalities for trigonometric polynomials with special coefficients.