Displaying similar documents to “Two-variable zeta functions and regularized products.”

Some mean convergence and complete convergence theorems for sequences of m -linearly negative quadrant dependent random variables

Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2013)

Applications of Mathematics

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The structure of linearly negative quadrant dependent random variables is extended by introducing the structure of m -linearly negative quadrant dependent random variables ( m = 1 , 2 , ⋯ ). For a sequence of m -linearly negative quadrant dependent random variables { X n , n ≥ 1 } and 1 < p < 2 (resp. 1 ≤ p < 2 ), conditions are provided under which n - 1 / p ∑ k = 1 n ( X k - E X k ) → 0 in L 1 (resp. in L p ). Moreover, for 1 ≤ p < 2 , conditions are provided under which n - 1 / p ∑ k = 1 n ( X k - E X k ) converges completely to 0 . The current work extends some results of Pyke and Root (1968) and it extends and...

On a quadratically convergent method using divided differences of order one under the gamma condition

Ioannis Argyros, Hongmin Ren (2008)

Open Mathematics

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We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide...