Functional Equations, Difference Inequalities and Ulam Stability Notions (F.U.N.) (Mathematics Research Developments)

✍ Scribed by John Michael Rassias

• Publisher: Nova Science Pub Inc
• Year: 2010
• Tongue: English
• Leaves: 223
• Series: Mathematics Research Developments
• Category: Library

✦ Synopsis

This book is a forum for exchanging ideas among eminent mathematicians and physicists, from many parts of the world, as a tribute to the first centennial birthday anniversary of Stanislaw Marcin ULAM. This collection is composed of outstanding contributions in mathematical and physical equations and inequalities and other fields of mathematical and physical sciences. It is intended to boost the co-operation among mathematicians and physicists working on a broad variety of pure and applied mathematical areas. This transatlantic collection of mathematical ideas and methods comprises a wide area of applications in which equations, inequalities and computational techniques pertinent to their solutions play a core role. Ulam's influence has been tremendous on our everyday life, because new tools have been developed, and revolutionary research results have been achieved , bringing scientists of exact sciences even closer, by fostering the emergence of new approaches, techniques and perspectives.

✦ Table of Contents

FUNCTIONAL EQUATIONS, DIFFERENCE INEQUALITIES AND ULAM STABILITY NOTIONS (F.U.N.)......Page 5
CONTENTS......Page 7
PREFACE......Page 9
1.Introduction......Page 13
2.Solutionof(1.1)......Page 15
3.Ulam’sStabilityfortheFunctionalEquation(1.1)......Page 16
References......Page 25
Abstract......Page 27
1.Introduction......Page 28
2.TheInitialPhaseoftheGame......Page 33
3.TheDevelopmentofGame1aftert0......Page 36
4.TheRestrictedRandomWalk......Page 41
5.TheFinalPhase......Page 43
1.Introduction......Page 49
2.Results......Page 51
References......Page 58
1.Introduction......Page 59
2.The
Result......Page 60
References......Page 64
1.Introduction......Page 67
2.Quadratic
Homomorphisms......Page 71
3.Quadratic
Derivations......Page 75
References......Page 79
Abstract......Page 85
1. Introduction......Page 86
2. Green's Formulas......Page 87
3. Fundamental Solutions......Page 89
4. Logarithmic Singularities of Fundamental Solutions......Page 93
References......Page 95
1.Introduction......Page 97
2.The Pointwise Superstability and Superstability of the Jordan E
quation......Page 100
References......Page 104
Introduction......Page 107
Statement of the Problem......Page 108
Uniqueness of the Solution of Problem GF......Page 109
Existence of the Solution of Problem GF......Page 110
References......Page 117
1.Introduction......Page 119
2.Functional Inequalities in Normed Modules over a C
∗-Algebra......Page 121
3.
Generalized Hyers–Ulam Stability of Functional I nequalities......Page 123
References......Page 127
1.Introduction and
Preliminaries......Page 131
2.On the Stability of Cubic Derivations on Banach
Modules......Page 133
3.On the Stability of Quartic Derivations on Banach
Modules......Page 136
References......Page 140
1. Introduction......Page 143
2. Tetrahedron Perimeter Isometry Stability......Page 147
References......Page 153
1.Introduction......Page 155
2.Cauchy Type Additive Functional
Equations......Page 156
References......Page 159
Abstract......Page 161
1. Introduction......Page 162
2. General Solution of the Functional Equation (1.10)......Page 165
3. Generalized Ulam Stability of the Functional Equation (1.10)......Page 168
4. Mixed Type Product – Sum Stability of FunctionalEquation (1.10)......Page 180
References......Page 184
1.Mappings Approximately Preserving
Orthogonality......Page 189
1.1.Orthogonality in Normed
Spaces......Page 193
2.Stability of the Orthogonality
Equation......Page 195
2.1.The case
p=1......Page 196
3.Stability of the Wigner
Equation......Page 199
References......Page 200
1.Formulation of Tricomi Problem for Mixed
Equations......Page 203
2.Representation of Solutions of Tricomi Problem for Mixed
Equations......Page 207
3.Existence of Solutions of Tricomi Problem for Mixed
Equations......Page 211
4.The Frankl Problem for Mixed Equations......Page 215
References......Page 219
INDEX......Page 221