Advances in Inequalities of the Schwarz, Grüss, and Bessel Type in Inner Product Spaces

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More About This Book

Product Details

  • ISBN-13: 9781594542022
  • Publisher: Nova Science Publishers, Incorporated
  • Publication date: 4/30/2005
  • Pages: 249

Table of Contents

Ch. 1 Reverses for the Schwarz inequality 1
1 Introduction 1
2 An additive reverse of the Schwarz inequality 2
3 A generalisation of the Cassels inequality 9
4 Quadratic reverses of Schwarz's inequality 18
5 More reverses of Schwarz's inequality 27
Ch. 2 Inequalities of the Gruss type 37
1 Introduction 37
2 Gruss' inequality in inner product spaces 41
3 Companions of Gruss' inequality 52
4 Other Gruss type inequalities 61
Ch. 3 Reverses of Bessel's inequality 71
1 Introduction 71
2 Reverses of Bessel's inequality 72
3 Another reverse for Bessel's inequality 84
4 More reverses of Bessel's inequality 97
5 General reverses of Bessel's inequality 109
Ch. 4 Generalisations of Bessel's inequality 125
1 Boas-Bellman type inequalities 125
2 Bombieri type inequalities 134
3 Pecaric type inequalities 148
Ch. 5 Some Gruss' type inequalities for n-tuples of vectors 161
1 Introduction 161
2 The version for norms 163
3 The version for inner-products 177
4 More Gruss' type inequalities 184
5 Some inequalities for forward difference 193
6 Bounds for a pair of n-tuples of vectors 201
Ch. 6 Other inequalities in inner product spaces 217
1 The Ostrowski inequality 217
2 Another Ostrowski type inequality 221
3 The Wagner inequality in inner product spaces 224
4 A monotoniciy property of Bessel's inequality 227
5 Other Bombieri type inequalities 230
6 Some pre-Gruss inequalities 235
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