Some mixed weak type inequalities

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

On Inequalities of Weak Type

for every f (x) in L(X) and A > 0 . Conclusions of this sort are called inequalities of weak type, or, where T*f(x) = supn | Tnf(x) | = r*(#, ƒ), that the operator T* is of weak type (p, p). Inequality (1) has often appeared with convergence a.e. in analysis, but a single result of this generality, predicting (1) as a consequence of convergence, had never before been obtained. Indeed, it seems ...

Some Dido-type inequalities

Alan Siegel is the product of the Palo Alto public school system in California. He earned his B.S. in mathematics and his Ph.D. in computer science at Stanford University. He is presently the Deputy Chairman for the Department of Computer Science at New York University. His areas of specialty include the mathematical analysis of algorithms, probabilistic analysis, and lower bounds. He is also a...

Sharp Weak - Type ( 1 , 1 ) Martingale Inequalities

Let X be a Hilbert-space valued martingale and Y a real-valued supermartingale which are orthogonal and with Y diierentially subordinate to X. Then where the constant (2) is Catalan's constant whose approximate value is 0:915965594. The constant K is B. Davis' constant in the Kolmogorov's weak-type inequality for conjugate harmonic functions in the unit disk. The inequality is sharp.

Some New Hilbert’s Type Inequalities