D. S. Mitrinović

Inequalities involving functions and their integrals and derivatives

I. Landau-Kolmogorov and related inequalities.- II. An inequality ascribed to Wirtinger and related results.- III. Opials inequality.- IV. Hardys, Carlemans and related inequalities.- V. Hilberts and related inequalities.- VI. Inequalities of Lyapunov and of De la Vallee Poussin.- VII. Zmorovi?s and related inequalities.- VIII. Carlsons and related inequalities.- IX. Inequalities involving kernels.- X. Convolution, rearrangement and related inequalities.- XI. Inequalities of Caplygin type.- XII. Inequalities of Gronwall type of a single variable.- XIII. Gronwall inequalities in higher dimension.- XIV. Gronwall inequalities on other spaces: discrete, functional and abstract.- XV. Integral inequalities involving functions with bounded derivatives.- XVI. Inequalities of Bernstein-Mordell type.- XVII. Methods of proofs for integral inequalities.- XVIII. Particular inequalities.- Name Index.

Topics in polynomials : extremal problems, inequalities, zeros

General concept of polynomials elementary inequalities zeros of polynomials special classes of polynomials extremal problems for polynomials inequalities connected with trigonometric sums.

Recent advances in geometric inequalities

The Existence of a Triangle.- Duality between Geometric Inequalities and Inequalities for Positive Numbers.- Homogeneous Symmetric Polynomial Geometric Inequalities.- Duality between Different Triangle Inequalities and Triangle Inequalities with (R, r, s).- Transformations for the Angles of a Triangle.- Some Trigonometric Inequalities.- Some Other Transformations.- Convex Functions and Geometric Inequalities.- Miscellaneous Inequalities with Elements of a Triangle.- Special Triangles.- Triangle and Point.- Inequalities with Several Triangles.- The Mobius-Neuberg and the Mobius-Pompeiu Theorems.- Inequalities for Quadrilaterals.- Inequalities for Polygons.- Inequalities for a Circle.- Particular Inequalities in Plane Geometry.- Inequalities for Simplexes in En (n ? 2).- Inequalities for Tetrahedra.- Other Inequalities in En (n ? 2).

Bernoulli’s Inequality

One of the most known elementary inequalities is Bernoullis inequality. This paper is a complete review on this important inequality.

About the Neuberg-Pedoe and the Oppenheim inequalities

Abstract This paper is a complete review and unified treatment of recent results conerning the Neuberg-Pedoe and Oppenheim inequalities. Some new proofs and generalizations of these results are also added.

Bessel’s Inequality

Let us consider the problem of the best approximation of a vector x by vectors of an orthonormal system from a Hilbert space X. For every system of numbers λ1,...,λ2 we have

Some Trigonometric Inequalities

||x - \sum\limits_{k = 1}^n {{\lambda _k}{x_k}|{|^2}} \geqslant 0.