Functional Equations, Inequalities and Applications

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics.

This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

Klappentext

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

Zusammenfassung

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics.

This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

Inhalt
1 HyersUlam stability of a quadratic functional equation in Banach modules.- 2 Cauchy and Pexider operators in some function spaces.- 3 The median principle for inequalities and applications.- 4 On the HyersUlamRassias stability of a Pexiderized quadratic equation II.- 5 On the HyersUlamRassias stability of a functional equation.- 6 A pair of functional inequalities of iterative type related to a Cauchy functional equation.- 7 On approximate algebra homomorphisms.- 8 Hadamard and DragomirAgarwal inequalities, the Euler formulae and convex functions.- 9 On Ulam stability in the geometry of PDE's.- 10 On certain functional equations and mean value theorems.- 11 Some general approximation error and convergence rate estimates in statistical learning theory.- 12 Functional equations on hypergroups.- 13 The generalized Cauchy functional equation.- 14 On the AleksandrovRassias problem for isometric mappings.