Remarks on Statistical and I-convergence of Series
ثبت نشده
چکیده
In this paper we investigate the relationship between the statistical (or generally I-convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B.C. Tripathy “On statistically convergent series”, Punjab.Univ. J.Math. 32 (1999), 1–8, is not correct.
منابع مشابه
On $I$-statistical and $I$-lacunary statistical convergence of order $alpha$
In this paper, following a very recent and new approach, we further generalize recently introduced summability methods, namely, $I$-statistical convergence and $I$-lacunary statistical convergence (which extend the important summability methods, statistical convergence and lacunary statistical convergence using ideals of $mathbb{N}$) and introduce the notions of $I$-statis...
متن کاملOn I-statistical Convergence
In the present paper, we investigate the notion of I -statistical convergence and introduce I -st limit points and I -st cluster points of real number sequence and also studied some of its basic properties.
متن کاملAchieving Regional Convergence through the Role of Foreign Direct Investment and Portfolio Investment: Evidence from ASEAN+3
T he purpose of this study is to analyze the effect of foreign direct investment and portfolio investment on the convergence occurrence of economic growth of countries in the ASEAN + 3 region and to determine the time or speed required to achieve convergence. The type of data used in this research is secondary data panel which is combination between time series data and cross-section...
متن کاملSome remarks on generalizations of classical prime submodules
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...
متن کاملRemarks on Distance-Balanced Graphs
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.
متن کامل