Means and Their Inequalities

1. Front Matter

   Pages i-xix

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2. Introduction

   • P. S. Bullen, D. S. Mitrinović, P. M. Vasić

   Pages 1-33

3. The Arithmetic, Geometric and Harmonic Means

   • P. S. Bullen, D. S. Mitrinović, P. M. Vasić

   Pages 34-131

4. The Power Means

   • P. S. Bullen, D. S. Mitrinović, P. M. Vasić

   Pages 132-214

5. The Quasi-Arithmetic Means

   • P. S. Bullen, D. S. Mitrinović, P. M. Vasić

   Pages 215-282

6. Symmetric Means

   • P. S. Bullen, D. S. Mitrinović, P. M. Vasić

   Pages 283-342

7. Further Means, Axiomatics and Other Topics

   • P. S. Bullen, D. S. Mitrinović, P. M. Vasić

   Pages 343-385

8. Back Matter

   Pages 387-459

   PDF

Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.

• filtering
• integrable system
• measure
• measure theory

• Department of Mathematics, University of British Columbia, Vancouver, Canada

  P. S. Bullen

• University of Belgrade, Yugoslavia

  D. S. Mitrinović, P. M. Vasić

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