This book examines new topics in the areas of fixed point theory, variational inequality and complementarity problem theory, non-linear ergodic theory, difference, differential and integral equations, control and optimisation theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications. Contents: Perturbed Version of a General Trapezoid Inequality; Perturbed Three-Point Rules; Three-Point Inequalities from Riemann-Stieltjes Integrals; Geometric Means, Index Mappings and Entropy; On Some Recent Results Related to Jessen's Inequality for Convex Functions; Estimates for an Integral in Lp Norm of the (n+1)-th Derivative of its Integrand; Some Refinements of the Triangle and Cauchy-Schwartz Inequalities in Inner Product Spaces; On the Algebraic Character of Blundon's Inequalities; The Jensen's Equation in Banach Modules over a C-Algebra; Improved Weighted Ostrowski-Gruss Type Inequalities; Sequences Supplied by Inequalities and Applications; Inequalities on Polynomial Divisors; Chebyshev-Anderson's Inequality; Convexity of the Gamma Function with Respect to Holder Means; Generalised Perturbed Inequalities of Ostrowski Type and Appl

This book introduces and exchanges recent innovative topics on the areas of fixed point theory, convex and set-valued analysis, variational inequality and complementarity problem theory, non-linear ergodic theory, difference, differential and integral equations, control and optimisation theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications.

This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. ... This work is a valuable resource!” (Mathematical Reviews). “The authors ... present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of ... Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.

The aim of this volume is to introduce and exchange recent new topics on the areas of inequality theory and their applications dealing in pure and applied mathematics.

This book introduces and exchanges recent innovative topics on the areas of fixed point theory, convex and set-valued analysis, variational inequality and complementarity problem theory, nonlinear ergodic theory, difference, differential and integral equations, control and optimization theory, dynamic system theory, inequality theory, stochastic analysis and probability theory, and their applications.

Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyone wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.