A variation on strong lacunary quasi-Cauchy sequences in 2-normed spaces

2015 ◽  
Author(s):  
Huseyin Cakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Spaces ◽  
Cauchy Sequences

scholarly journals Strongly Lacunary Ward Continuity in 2-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hüseyin Çakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A functionfdefined on a subsetEof a 2-normed spaceXis strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points inE; that is,(f(xk))is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

scholarly journals On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Normed Space ◽  
Complex Numbers ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Cauchy Sequences ◽  
Limit Points ◽  
Positive Integers ◽  
Cluster Points

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

scholarly journals Lacunary ward continuity in 2-normed spaces

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2257-2263 ◽  
Author(s):  
Huseyin Cakalli ◽  
Sibel Ersan
Keyword(s):  
Real Number ◽  
Normed Space ◽  
Positive Real Number ◽  
Normed Spaces ◽  
Positive Real ◽  
Cauchy Sequences ◽  
Positive Integers

In this paper, we introduce lacunary statistical ward continuity in a 2-normed space. A function f defined on a subset E of a 2-normed space X is lacunary statistically ward continuous if it preserves lacunary statistically quasi-Cauchy sequences of points in E where a sequence (xk) of points in X is lacunary statistically quasi-Cauchy if limr?1 1/hr |{k?Ir : ||xk+1 - xk, z||? ?}| = 0 for every positive real number ? and z ? X, and (kr) is an increasing sequence of positive integers such that k0 = 0 and hr = kr - kr-1 ? ? as r ? ?, Ir = (kr-1, kr]. We investigate not only lacunary statistical ward continuity, but also some other kinds of continuities in 2-normed spaces.

scholarly journals On S-normed spaces

2019 ◽  
Vol 24 (4) ◽  
pp. 82 ◽  
Author(s):  
Shahen M. Ali ◽  
Laith K. Shaakir
Keyword(s):  
Linear Transformation ◽  
Normed Space ◽  
Normed Spaces ◽  
Cauchy Sequences

The study focused on expanding the concept of 2-normed spaces by developing a new definition ( -normed space), and the study concentrated on the convergent of sequences and Cauchy sequences in our definition, as well as some other branches such as linear transformation and contraction.   http://dx.doi.org/10.25130/tjps.24.2019.078

scholarly journals Generalized ideal convergence in intuitionistic fuzzy normed linear spaces

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 811-820 ◽  
Author(s):  
Bipan Hazarika ◽  
Vijay Kumar ◽  
Bernardo Lafuerza-Guilién
Keyword(s):  
Real Number ◽  
Normed Spaces ◽  
Real Numbers ◽  
Ideal Convergence ◽  
Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Cauchy Sequences ◽  
Positive Integers ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Cluster Points

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 [19], 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 e, if for each ? > 0 the set {k ? N : |xk - e| ? ?} belongs to I. The aim of this paper is to introduce and study the notion of ?-ideal convergence in intuitionistic fuzzy normed spaces as a variant of the notion of ideal convergence. Also I? -limit points and I?-cluster points have been defined and the relation between them has been established. Furthermore, Cauchy and I?-Cauchy sequences are introduced and studied. .

scholarly journals Ward continuity in 2-normed spaces

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1507-1513 ◽  
Author(s):  
Sibel Ersan ◽  
Hüseyin Çakalli
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Cauchy Sequences

In this paper, we introduce and investigate the concept of ward continuity in 2-normed spaces. A function f defined on a 2-normed space (X,?.,.?) is ward continuous if it preserves quasi-Cauchy sequences, where a sequence (xn) of points in X is called quasi-Cauchy if limn?1 ??xn,z? = 0 for every z ? X. Some other kinds of continuities are also introduced, and interesting theorems are proved in 2-normed spaces.

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