TITLE

A variation on Abel quasi Cauchy sequences

AUTHOR(S)
Çakallı, Hüseyin
PUB. DATE
September 2015
SOURCE
AIP Conference Proceedings;2015, Vol. 1676 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we introduce and investigate the concept of Abel ward continuity. A real function ƒ is Abel ward continuous if it preserves Abel quasi Cauchy sequences, where a sequence (pk) of point in R is called Abel quasi-Cauchy if the series Σk=0∞△pk·xk is convergent for 0 ≤ x < 1 and limx→1-(1-x)Σk=0∞△pk·xk=0, where → pk = pk+1 - pk for every non negative integer k. Some other types of continuities are also studied and interesting results are obtained. It turns out that uniform limit of a sequence of Abel ward continuous functions is Abel ward continuous and the set of Abel ward continuous functions is a closed subset of the set of continuous functions.
ACCESSION #
109578203

 

Related Articles

  • Statistically pre-Cauchy Fuzzy real-valued sequences defined by Orlicz function. Dutta, Amar Jyoti; Tripathy, Binod Chandra // Proyecciones - Journal of Mathematics;Sep2014, Vol. 33 Issue 3, p235 

    In this article we have defined statistically pre-Cauchy sequence of fuzzy real numbers defined by Orlicz function. We have proved a necessary and sufficient condition for a sequence X = (Xk) of fuzzy real numbers to be statistically pre-Cauchy. We have also established some other results.

  • Lacunary Ideal Convergence of Double Set Sequences. Kişi, Ömer // General Mathematics Notes;Aug2015, Vol. 29 Issue 2, p36 

    In this paper the relation between lacunary ideal convergent double set se- quences and lacunary ideal Cauchy double set sequences has been established. The notions of lacunary ideal limit sets and lacunary ideal cluster sets have been introduced and find the relation between these two notions.

  • On strongly I and I*-lacunary convergence of sequences of sets. Sever, Yurdal; Ulusu, Uğur; Dündar, Erdinç // AIP Conference Proceedings;2014, Vol. 1611, p357 

    In this paper we study the concepts of Wijsman strongly lacunary convergence, Wijsman strongly I-lacunary convergence, Wijsman strongly I*-lacunary convergence and Wijsman strongly I-lacunary Cauchy sequences of sets and investigate the relationship between them.

  • A variation on Abel statistical ward continuity. Cakalli, Huseyin; Taylan, Iffet // AIP Conference Proceedings;2015, Vol. 1676 Issue 1, p1 

    A real valued function f defined on a subset of R, the set of real numbers is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (ak) of point in R is called Abel statistically quasi-Cauchy if Abel density of the set {k ∞ N :...

  • On ideal convergence in topological groups. Hazarika, Bipan // Scientia Magna;2011, Vol. 7 Issue 4, p42 

    An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [9], Kostyrko et. al introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number xo, if for each ε...

  • Lacunary statistically upward half quasi-Cauchy sequences. Cakalli, Huseyin; Mucuk, Osman // AIP Conference Proceedings;2015, Vol. 1676 Issue 1, p1 

    A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (xn) of points in R is called lacunary statistically upward half quasi-Cauchy if ......

  • TWO-NORM CONVERGENCE IN THE Lp SPACES. Indrati, Ch. Rini // Real Analysis Exchange;2011/2012, Vol. 37 Issue 1, p55 

    In this paper we consider Lp, 1 ≤ p ≤ ∞, as a two-norm space and prove a representation for two-norm continuous functionals defined on Lp, 1 ≤ p ≤ ∞. Hence we have provided a unified approach for the scale of the Lp space, including the case when p = ∞.

  • New Convergence Definitions for Sequences of Sets. Kişi, Ömer; Nuray, Fatih // Abstract & Applied Analysis;2013, p1 

    Several notions of convergence for subsets of metric space appear in the literature. In this paper, we define Wijsman I-convergence and Wijsman I*-convergence for sequences of sets and establish some basic theorems. Furthermore, we introduce the concepts of Wijsman I-Cauchy sequence and Wijsman...

  • ON A SPECIAL SUBCLASS OF THE SET OF DERIVATIVES. Menkyna, Robert // Real Analysis Exchange;2006/2007, Vol. 32 Issue 1, p79 

    We deal with the class of functions defined as a sum of a uniformly convergent series of functions continuous both on a closed set and on its complement. Such functions are mentioned in the literature, e.g., in [1], [2], [3], [4]. We investigate the particular class of derivatives.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics