Search results for: general-inequalities-2

General Inequalities 2

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General Inequalities 7

Author : Catherine Bandle
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Inequalities continue to play an essential role in mathematics. The subject is per haps the last field that is comprehended and used by mathematicians working in all the areas of the discipline of mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities. New inequalities are discovered ev ery year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. So extensive are these developments that a new mathematical periodical devoted exclusively to inequalities will soon appear; this is the Journal of Inequalities and Applications, to be edited by R. P. Agar wal. Nowadays it is difficult to follow all these developments and because of lack of communication between different groups of specialists many results are often rediscovered several times. Surveys of the present state of the art are therefore in dispensable not only to mathematicians but to the scientific community at large. The study of inequalities reflects the many and various aspects of mathemat ics. There is on the one hand the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand the subject is a source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are many applications in a wide variety of fields from mathematical physics to biology and economics.

General Inequalities 5

Author : WALTER
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The Fifth International Conference on General Inequalities was held from May 4 to May 10, 1986, at the Mathematisches Forschungsinstitut Oberwolfach (Black Forest, Germany). The organizing committee consisted of W.N. Everitt (Birmingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec served efficiently an'd enthusiastically as secretary to the con ference. The meeting was attended by 50 participants from 16 countries. In his opening address, W. Walter had to report on the death of five colleagues who had been active in the area of inequali ties and who had served the mathematical community: P.R. Beesack, G. Polya, D.K. Ross, R. Bellman, G. Szegö. He made special mention of G. Polya, who had been the last surviving author of the book InequaZities (Cambridge University Press, 1934), who died at the age of 97 years and whose many and manifold contributions to mathematics will be recorded elsewhere, in due course. Inequalities continue to play an important and significant role in nearly all areas of mathematics. The interests of the participants to this conference reflected the many different fields in which both classical and modern inequalities continue to influence developments in mathematics. In addition to the established fields, the lectures clearly indicated the importance of inequalities in functional analysis, eigenvalue theory, con vexi ty., number theory, approximation theory, probability theory, mathematical prograrnrning and economics.

General Inequalities 6

Author : Wolfgang Walter
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The sixthInternational Conference on General Inequalities was held from Dec. 9 to Dec. 15, 1990, at the Mathematisches Forschungsinstitut Oberwolfach (Black Fa rest, Germany). The organizing committee was composed of W.N. Everitt (Birm ingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec ( Coimbra) served cheerfully and efficiently as secretary of the meeting. The con ference was attended by 44 participants from 20 countries. Yet again the importance of inequalities in both pure and applied mathematics was made evident from the wide range of interests of the individual participants, and from the wealth of new results announced. New inequalities were presented in the usual spread of the subject areas now expected for these meetings: Classical and functional analysis, existence and boundary value problems for both ordinary and partial differential equations, with special contributions to computer science, quantum holography and error analysis. More strongly than ever, the role played by modern electronic computers was made clear in testing out and prohing into the validity and structure of certain inequalities. Here the computer acts not only for numerical calculations of great complexity, but also in symbolic manipulation of complex finite structures. Prob lems in inequalities which even a few years ago were intractable, now fall to solution or receive direct and positive guidance as a result of computer applications. The interface between finite and infinite structures in mathematics and the versatility of modern computers is weil developed in the subject of general inequalities.

Inequalities Involving Functions and Their Integrals and Derivatives

Author : Dragoslav S. Mitrinovic
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One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.

Neutrosophic Variational Inequalities with Applications in Decision Making

Author : Madad Khan
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In this paper, we introduced some new concepts of a neutrosophic set such as neutrosophic convex set, strongly neutrosophic convex set, neutrosophic convex function, strongly neutrosophic convex function, the minimum and maximum of a function f with respect to neutrosophic set, min and max neutrosophic variational inequality, neutrosophic general convex set, neutrosophic general convex function and min, max neutrosophic general variational inequality.

Inequalities for Graph Eigenvalues

Author : Zoran Stanić
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Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, Seidel matrix, and distance matrix. The book begins with a brief survey of the main results and selected applications to related topics, including chemistry, physics, biology, computer science, and control theory. The author then proceeds to detail proofs, discussions, comparisons, examples, and exercises. Each chapter ends with a brief survey of further results. The author also points to open problems and gives ideas for further reading.

Hardy Type Inequalities for Abstract Differential Operators

Author : Werner O. Amrein
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This paper is concerned with certain estimates on the asymptotic behaviour of the functions [italic]u defined on an interval (a, [infinity symbol]) with values in a Hilbert space [italic]H. More precisely, if [italic]L is a second order ordinary differential operator the coefficients of which are operators acting in [italic]H, we wish to obtain inequalities allowing one to get information about the behaviour of a function [italic]u in a neighborhood of infinity from the asymptotic behaviour of the function [italic]L[italic]u. These inequalities will be called Hardy type inequalities.


Author : Edwin F. Beckenbach
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Since the elassie work on inequalities by HARDY, LITTLEWOOD, and P6LYA in 1934, an enonnous amount of effort has been devoted to the sharpening and extension of the elassieal inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us eite the fields of ordinary and partial differential equations, whieh are dominated by inequalities and variational prineiples involving functions and their derivatives; the many applications of linear inequalities to game theory and mathe matieal economics, which have triggered a renewed interest in con vexity and moment-space theory; and the growing uses of digital com puters, which have given impetus to a systematie study of error esti mates involving much sophisticated matrix theory and operator theory. The results presented in the following pages reflect to some extent these ramifications of inequalities into contiguous regions of analysis, but to a greater extent our concem is with inequalities in their native habitat. Since it is elearly impossible to give a connected account of the burst of analytic activity of the last twenty-five years centering about inequalities, we have d. eeided to limit our attention to those topies that have particularly delighted and intrigued us, and to the study of whieh we have contributed.

Means and Their Inequalities

Author : P.S. Bullen
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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.