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Levinson's Inequality
In mathematics, Levinson's inequality is the following inequality, due to Norman Levinson, involving positive numbers. Let a>0 and let f be a given function having a third derivative on the range (0,2a), and such that :f(x)\geq 0 for all x\in (0,2a). Suppose 0 |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize (after winning in 1970 the Lester R. Ford Award) of the Mathematical Association of America for his paper ''A Motivated Account of an Elementary Proof of the Prime Number Theorem''. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey. He received both his bachelor's degree and his master's degree in electrical engineering f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ky Fan Inequality
In mathematics, there are two different results that share the common name of the Ky Fan inequality. One is an inequality involving the geometric mean and arithmetic mean of two sets of real numbers of the unit interval. The result was published on page 5 of the book ''Inequalities'' by Edwin F. Beckenbach and Richard E. Bellman (1961), who refer to an unpublished result of Ky Fan. They mention the result in connection with the inequality of arithmetic and geometric means and Augustin Louis Cauchy's proof of this inequality by forward-backward-induction; a method which can also be used to prove the Ky Fan inequality. This Ky Fan inequality is a special case of Levinson's inequality and also the starting point for several generalizations and refinements; some of them are given in the references below. The second Ky Fan inequality is used in game theory to investigate the existence of an equilibrium. Statement of the classical version If with 0\le x_i\le \frac for ''i'' = 1, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
