Results 1 to 10 of about 21,951 (149)

Ideal-quasi-Cauchy sequences [PDF]

Journal of Inequalities and Applications, 2012
An ideal $I$ is a family of subsets of positive integers $\textbf{N}$ which is closed under taking finite unions and subsets of its elements.
Cakalli, Huseyin, Hazarika, Bipan
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A Study on -Quasi-Cauchy Sequences [PDF]

Abstract and Applied Analysis, 2013
Recently, the concept of -ward continuity was introduced and studied. In this paper, we prove that the uniform limit of -ward continuous functions is -ward continuous, and the set of all -ward continuous functions is a closed subset of the set of all ...
Hüseyin Çakalli, Huseyin Kaplan
doaj   +3 more sources

A new study on the strongly lacunary quasi Cauchy sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018
In this paper, the concept ofan -quasi-Cauchysequence is introduced. We proved interesting theorems related to -quasi-Cauchysequences. A real valued function defined on a subset of , the set of real numbers, is -ward continuous on if it preserves -quasi ...
Huseyin Cakalli, Hüseyin Kaplan
doaj   +3 more sources

On certain new notion of order Cauchy sequences, continuity in (l)-group

Applied General Topology, 2022
In this paper, we introduce the notion order quasi-Cauchy se-quences, downward and upward order quasi-cauchy sequences, order half Cauchy sequences.
Sudip Kumar Pal, Sagar Chakraborty
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Equivalent Cauchy Sequences in q1,q2-Quasi Metric-Like Space and Applications to Fixed-Point Theory

Journal of Mathematics, 2021
This paper introduces the concept of q1,q2-quasi metric-like space X,p and delves into some topological properties of it. A necessary and sufficient condition related to equivalent Cauchy sequences and Cauchy sequences in X,p have been proved ...
Eriola Sila, Sidite Duraj, Elida Hoxha
doaj   +1 more source

Sequential Completeness for ⊤-Quasi-Uniform Spaces and a Fixed Point Theorem

Mathematics, 2022
We define sequential completeness for ⊤-quasi-uniform spaces using Cauchy pair ⊤-sequences. We show that completeness implies sequential completeness and that for ⊤-uniform spaces with countable ⊤-uniform bases, completeness and sequential completeness ...
Gunther Jäger
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Completion of continuity spaces with uniformly vanishing asymmetry [PDF]

, 2014
The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in question.
Chand, Alveen, Weiss, Ittay
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Strongly Lacunary Ward Continuity in 2-Normed Spaces

The Scientific World Journal, 2014
A function f defined on a subset E of a 2-normed space X is strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points in E; that is, (f(xk)) is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly
Hüseyin Çakalli, Sibel Ersan
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𝑁𝜃-Ward Continuity

Abstract and Applied Analysis, 2012
A function 𝑓 is continuous if and only if 𝑓 preserves convergent sequences; that is, (𝑓(𝛼𝑛)) is a convergent sequence whenever (𝛼𝑛) is convergent. The concept of 𝑁𝜃-ward continuity is defined in the sense that a function 𝑓 is 𝑁𝜃-ward continuous if it ...
Huseyin Cakalli
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Some Fixed-Point Theorems on Quasi M-Metric Spaces [PDF]

ITM Web of Conferences
In this paper, it will be discussed a metric that is constructed based on a quasi M-metric and a new definition of Cauchy sequences in quasi M-metric spaces.
Darojad Rofiud, Indrati Christiana Rini
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