Search

© 2022 American Institute of Physics Inc.. All rights reserved.Sequential convergence is quite useful to define some topological notions. As a generalization of convergences of sequences a G-method is defined in [13] by Connor and Grosse-Erdmann to be a real valued function defined on a linear subspace of the vector space of all real sequences. Based on this definition some authors have introduced the concepts G-compactness and G-connectedness for topological groups. In this work we consider G-methods on product spaces; and characterise the G-connectedness of product topological spaces with some results.

In this extended abstract, we modify the definition of h-open set introduced in [1] by F. Abbas who neglects that the set of all h-open sets is a topology, and we show that the union of any family of h-open subsets of X is h-open that ensures that the set of all h-open subsets of a topological space (X, τ) forms a topology which is finer than τ, where a subset A of a topological space (X, τ) is said to be h-open if A ⊆ Int(A ∪ U) for every non-empty subset U of X such that U ∈ τ. We also give continuity type theorems. © 2022 American Institute of Physics Inc.. All rights reserved.

In this study, we investigate the concepts of Abel statistical convergence and Abel statistical quasi Cauchy sequences. A function f from a subset E of a metric space X into X is called Abel statistically ward continuous it preserves Abel statistical quasi Cauchy sequences, where a sequence (xk) of point in E is called Abel statistically quasi Cauchy if limx→1− (1 − x) ∑ k:d(xk+1,xk)≥ε x k = 0 for every ε > 0. Some other types of continuities are also studied and interesting results are obtained.

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (α, β) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (α, β) is also investigated. Interesting results are obtained.

On behalf of the Organizing Committee, we are very pleased to welcome you to the 3nd International Confer- ence of Mathematical Sciences (ICMS 2019) to be held between 4-8 September 2019 at Maltepe University in Istanbul. We hope that, ICMS 2019 will be one of the most beneficial scientific events, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in any field of science.

A sequence (αk) of points in R, the set of real numbers, is called ρ-statistically convergent to an element ℓ of R of order β if limn→∞ 1 ρ β n |{k ≤ n : |αk − ℓ| ≥ ε}| = 0 for each ε > 0, where ρ = (ρn) is a non-decreasing sequence of positive real numbers tending to ∞ such that lim supn ρn n < ∞, ∆ρn = O(1), and ∆αn = αn+1 − αn for each positive integer n. A real-valued function defined on a subset of R is called ρ-statistically ward continuous if it preserves ρ-statistical quasi Cauchy sequences where a sequence (αk) is defined to be ρ-statistically quasi-Cauchy if the sequence (∆αk) is ρ-statistically convergent to 0. We obtain results related to ρ-statistical ward continuity, ρ-statistical ward compactness, ward continuity, continuity, and uniform continuity

In this study, we introduce a concept of statistical quasi-Cauchyness of a sequences in a cone metric space in the sense that a sequence (xk) is statistically quasi-Cauchy if limn→∞ 1 n |{k ≤ n : d(xk+1, xk) ≥ c}| = 0 for each c ∈ P 0 . It turns out that a real valued function f is uniformly continuous either on a totally bounded subset of a cone metric space X or on a connected subset of X if f preserves statistical quasi-Cauchy sequences

Cakalli extended the concept of G−sequential compactness to a fuzzy topological group and introduced the notion of G−fuzzy sequential compactness, where G is a function from a suitable subset of the set of all sequences of fuzzy points in a fuzzy first countable topological space X. The aim of this paper is to investigate whether an idea like the G−fuzzy continuity can be introduced and consequently can be extended to a more general approach to fuzzy continuity in fuzzy topological spaces. In this article, we introduce the concepts of G−fuzzy sequential continuity and G−fuzzy sequential closedness in a fuzzy topological space and give some characterization theorems.

In Cakalli a sequence (x (k)) in a topological group X is called statistically convergent to an element 1 of X if for each neighbourhood U of 0 limmnm m-1|{ksm: x (k)-16, 2 U}|= 0 where the vertical bars indicate the number of elements in the enclosed set. This concept was first given by Fast2 and studied by Fridy3, Kolk6 and Maddox”.

In 2007, the concept of cone metric space was introduced by Huang Long-Guang and Zhang Xian. Recently Sönmez introduce the concept of cone normed space. Some topological properties of cone metric spaces was recently given by Türkoğlu, D. and Abuloha M. In this note, we give some more properties of cone metric spaces and prove related theorems.

In case of ordinary normed spaces, completion of a normed space is well-known. In 2007, the concept of cone metric space was introduced by Huang Long-Guang and Zhang Xian. Recently Sonmez introduce the concept of cone normed space. In this note, we construct completion of cone normed spaces, and prove that any cone normed space can be completed.