منابع مشابه
The Converse Ostrowski Theorem: aspects of compactness
The Ostrowski theorem in question is that an additive function bounded (above, say) on a set T of positive measure is continuous. In the converse direction, recall that a topological space T is pseudocompact if every function continuous on T is bounded. Thus theorems of converse Ostrowskitype relate to additive (pseudo)compactness. We give a di¤erent characterization of such sets, in terms ...
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Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B ⊆ A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the (non-commutative) base algebra of H, relative injectivity of the H-comodule algebra A is related to the Galois property of the extension B ⊆ A and also to the equivalence of the category of relative Hopf...
متن کاملPositive Operators and an Inertia Theorem
In recent years there has been interest in a theorem on positive definite matrices known as Lyapunov's theorem. Several authors have proved generalizations of this theorem, (WIELANDT [29J, TAUSSKY [24J, [25J, [26J , OSTROWSKISCHNEIDER [20J, GIVENS [10J, CARLSON-SCHNEIDER [3J, CARLSON [4J) . Lyapunov's theorem and its generalizations have become known as inertia theorems. In this note we shall u...
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(b− a)M, for all x ∈ [a, b] . The constant 14 is best possible in the sense that it cannot be replaced by a smaller constant. In [2], the author has proved the following Ostrowski type inequality. Theorem 2. Let f : [a, b] → R be continuous on [a, b] with a > 0 and differentiable on (a, b) . Let p ∈ R\ {0} and assume that Kp (f ) := sup u∈(a,b) { u |f ′ (u)| } < ∞. Then we have the inequality...
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Some Ostrowski type inequalities via Cauchy’s mean value theorem and applications for certain particular instances of functions are given.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1973
ISSN: 0022-247X
DOI: 10.1016/0022-247x(73)90190-x