A refinement of various mean inequalities.
Hara, Takuya, Uchiyama, Mitsuru, Takahasi, Sin-Ei (1998)
Journal of Inequalities and Applications [electronic only]
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Hara, Takuya, Uchiyama, Mitsuru, Takahasi, Sin-Ei (1998)
Journal of Inequalities and Applications [electronic only]
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Retkes, Z. (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Kangkang Wang (2009)
Czechoslovak Mathematical Journal
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In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system...
Rojo, Oscar (2006)
Journal of Inequalities and Applications [electronic only]
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Li, Gaorong, Chen, Shuang, Feng, Sanying (2008)
Journal of Applied Mathematics
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Cirtoaje, Vasile (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Wei Guo Yang, Zhong Xing Ye, Liu, Wen (2006)
Czechoslovak Mathematical Journal
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In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.
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...