Related papers: A new variation on statistical ward continuity
A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is statistically upward continuous if it preserves statistically upward half quasi-Cauchy sequences, is statistically downward continuous if it…
In this paper, we introduce a concept of statistically $p$-quasi-Cauchyness of a real sequence in the sense that a sequence $(\alpha_{k})$ is statistically $p$-quasi-Cauchy if $\lim_{n\rightarrow\infty}\frac{1}{n}|\{k\leq n:…
A function $f$ defined on a subset $E$ of a two normed space $X$ is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in $E$ where a sequence $(x_n)$ is statistically quasi-Cauchy if $(\Delta…
The main object of this paper is to investigate $\lambda$-statistically quasi-Cauchy sequences. A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is called $\lambda$-statistically ward continuous…
In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function $f$ on a subset $E$ of $\R$, the set of real numbers is down continuous if it preserves downward half Cauchy sequences,…
A real function $f$ is ward continuous if $f$ preserves quasi-Cauchyness, i.e. $(f(x_{n}))$ is a quasi-Cauchy sequence whenever $(x_{n})$ is quasi-Cauchy; and a subset $E$ of $\textbf{R}$ is quasi-Cauchy compact if any sequence…
The main object of this paper is to investigate lacunary statistically ward continuity. We obtain some relations between this kind of continuity and some other kinds of continuities. It turns out that any lacunary statistically ward…
In this paper we call a real-valued function $N_{\theta}$-ward continuous if it preserves $N_{\theta}$-quasi-Cauchy sequences where a sequence $\boldsymbol{\alpha}=(\alpha_{k})$ is defined to be $N_{\theta}$-quasi-Cauchy when the sequence…
A function $f$ defined on a 2-normed space $ (X,||.,.||)$ is ward continuous if it preserves quasi-Cauchy sequences where a sequence $(x_n)$ of points in $X$ is called quasi-Cauchy if $lim_{n\rightarrow\infty}||\Delta x_{n},z||=0$ for every…
In this paper, the concept of an $N_{\theta}^{2}$ quasi-Cauchy sequence is introduced. We proved interesting theorems related to $N_{\theta}^{2}$-quasi-Cauchy sequences. A real valued function $f$ defined on a subset $A$ of $\mathbb{R}$,…
The s-th forward difference sequence that tends to zero, inspired by the consecutive terms of a sequence approaching zero, is examined in this study. Functions that take sequences satisfying this condition to sequences satisfying the same…
We introduce statistically $p$-upward quasi-Cauchy sequences, defined by the condition $\lim_{n\to\infty}\frac{1}{n}|\{k\leq n: x_k - x_{k+p}\geq\varepsilon\}|=0$ for every $\varepsilon>0$, and develop the corresponding notions of…
In this paper, we prove that any ideal ward continuous function is uniformly continuous either on an interval or on an ideal ward compact subset of $\textbf{R}$. A characterization of uniform continuity is also given via ideal quasi-Cauchy…
Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function $f$ is forward continuous if $\lim_{n\to\infty} \Delta f(x_{n})=0$ whenever $\lim_{n\to\infty} \Delta x_{n}=0$,\;…
In this paper we generalize the concept of a quasi-Cauchy sequence to a concept of a $p$-quasi-Cauchy sequence for any fixed positive integer $p$. For $p=1$ we obtain some earlier existing results as a special case. We obtain some…
A double sequence $\{x_{k,l}\}$ is quasi-Cauchy if given an $\epsilon > 0$ there exists an $N \in {\bf N}$ such that $$\max_{r,s= 1\mbox{ and/or} 0} \left \{|x_{k,l} - x_{k+r,l+s}|< \epsilon\right \} .$$ We study continuity type properties…
In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function $f$ is Abel statistically continuous on a subset $E$ of $\R$, the set of real numbers, if it preserves Abel statistical convergent…
A function between two metric spaces is said to be totally bounded regular if it preserves totally bounded sets. These functions need not be continuous in general. Hence the purpose of this article is to study such functions vis-\'a-vis…
Given a continuous real-valued function on [0, 1], and a closed subset E \subset [0, 1] we denote by f E the restriction of f to E, that is, the function defined only on E that takes the same values as f at every point of E >. The…
In this article we call a sequence $(a_n)_n$ of elements of a metric space nearly computably Cauchy if for every strictly increasing computable function $r:\mathbb{N}\to\mathbb{N}$ the sequence $(d(a_{r(n+1)},a_{r(n)}))_n$ converges…