Lacunary almost summability in certain linear topological spaces.
Lacunary convergence of series in L0 revisited.
A simpler proof is given for the recent result of I. Labuda and the author that a series in the space L0 (lambda) is subseries convergent if each of its lacunary subseries converges.
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.
Leibniz Series forπ
In this article we prove the Leibniz series for π which states that π4=∑n=0∞(−1)n2⋅n+1. The formalization follows K. Knopp [8], [1] and [6]. Leibniz’s Series for Pi is item 26 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.
Les bonnes moyennes uniformisantes et une application à la resommation réelle
Limit points of eigenvalues of truncated unbounded tridiagonal operators
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n}n=1∞, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T N. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
Linear matrix differential equations of higher-order and applications.
Local approximation properties of certain class of linear positive operators via I-convergence
In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.
Logarithmic matrix transformations into .
Lucid operators on Banach spaces