Orlicz–Pettis Theorem through Summability Methods [PDF]
Mathematics, 2019 This paper unifies several versions of the Orlicz−Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear ...
Fernando León-Saavedra +2 more
doaj +4 more sources
New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences [PDF]
Axioms, 2018 In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical ...
Ömer Kişi +2 more
doaj +2 more sources
Ideal Convergence Generated by Double Summability Methods
Demonstratio Mathematica, 2016 The main result of this note is that if I is an ideal generated by a regular double summability matrix summability method T that is the product of two nonnegative regular matrix methods for single sequences, then I-statistical convergence and convergence
Jeff Connor
exaly +2 more sources
Order Summability and Almost Convergence
Proceedings of the American Mathematical Society, 1973 The object of this paper is to compare the summability methods of almost convergence and order summability. This is done by examining a method of summability which includes both methods.
Howard T. Bell
exaly +2 more sources
LACUNARY STATISTICAL HARMONIC SUMMABILITY [PDF]
, 2022 In this paper, the concepts of lacunary (H,1) summability, lacunary strongly harmonically summability, lacunary statistical (H,1) summability, lacunary statistical logarithmic convergence of sequences of real numbers are introduced and relations between ...
Nuray, Fatih
core +1 more source
ON DISCRETE WEIGHTED STATISTICAL CONVERGENCE [PDF]
, 2021 In the present paper, the notion of discrete weighted mean method of summability isextended the concept of statistical convergence. We also give the notion of statistical (M,P_{λ})-summability and [M,P_{λ}]_{q}-summability.
Altin, Yavuz +5 more
core +1 more source
A generalized statistical convergence via ideals [PDF]
, 2011 In this paper we make a new approach to the notions of [V,λ]-summability and λ-statistical convergence by using ideals and introduce new notions, namely, I−[V,λ]-summability and I−λ-statistical convergence.
Ekrem Savas +3 more
core +1 more source
ON f− STATİSTİCAL CONVERGENCE OF FRACTİONAL DİFFERENCE ON DOUBLE SEQUENCES [PDF]
, 2022 In this paper, using the fractional difference operator and a modulus function we introduce the concepts of $({}^{}_{2}{\Delta_{\beta}^{\tilde{\alpha}}},f)-$ statistical convergence, $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ statistical Cauchy and p ...
Atabey, Koray İbrahim +1 more
core +1 more source
On generalizations of certain summability methods using ideals [PDF]
, 2011 In this paper, following the line of Savas and Das (2011) [10], we provide a new approach to two well-known summability methods by using ideals, introduce new notions, namely, I-statistical convergence and I-lacunary statistical convergence, investigate ...
Ekrem Savas +5 more
core +1 more source
Generalized summability methods of functions using ideals [PDF]
, 2015 International Conference on Advancements in Mathematical Sciences, AMS 2015 -- 5 November 2015 through 7 November 2015 -- -- 115706In this paper, we shall make a new approach to two well known summability methods by using ideals and introduce new notions,
Ekrem Savaş, Savaş, Ekrem
core +1 more source