Irrational rapidly convergent series
Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces.
Iterated series and the Hellinger-Toeplitz theorem.
We show that an iterated double series condition due to Antosik implies the uniform convergence of the double series. An application of Antosik's condition is given to the derivation of a vector form of the Hellinger-Toeplitz theorem.
Jeden způsob sumace divergentních řad
Jednoduchý příklad dvojnásobné řady, která nepřipouští výměnu pořadu summačního
Konvergenz von Teilen der harmonischen Reihe.
Lacunary almost summability in certain linear topological spaces.
Lacunary equi-statistical convergence of positive linear operators
In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation...
Lacunary statistical convergence and inclusion properties between lacunary methods.
Lacunary strong -convergence
The definition of lacunary strongly convergence is extended to the definition of lacunary strong -convergence with respect to invariant mean when is an infinite matrix and is a strictly positive sequence. We study some properties and inclusion relations.
Lacunary strong convergence with respect to a sequence of modulus functions
The definition of lacunary strong convergence is extended to a definition of lacunary strong convergence with respect to a sequence of modulus functions in a Banach space. We study some connections between lacunary statistical convergence and lacunary strong convergence with respect to a sequence of modulus functions in a Banach space.
Lacunary weak statistical convergence
The aim of this work is to generalize lacunary statistical convergence to weak lacunary statistical convergence and -convergence to weak -convergence. We start by defining weak lacunary statistically convergent and weak lacunary Cauchy sequence. We find a connection between weak lacunary statistical convergence and weak statistical convergence.
Les bonnes moyennes uniformisantes et une application à la resommation réelle
Linear matrix differential equations of higher-order and applications.
Logarithmic matrix transformations into .
Maps preserving convergence of series
Matrix characterization of oscillation for double sequences
The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup(m,n)→∞;(α,β)→∞|S m,n-S α,β|. Using this concept a matrix characterization of double oscillation...
Matrix Transormations of Almost Convergent Sequenes. II.
Measure and category---some non-analogues.
Mediations on the product rule.