scholarly journals Ideal convergent sequences of functions in probabilistic normed spaces

2021 ◽  
Vol 26 (03) ◽  
pp. 249-254
Author(s):  
V. A. Khan ◽  
H. Altaf ◽  
M. Alam
Keyword(s):  
Normed Spaces ◽  
Probabilistic Normed Spaces ◽  
Convergent Sequences

scholarly journals On Asymptotically Double Lacunary Statistical Equivalent Sequences in Probabilistic Normed Space

2012 ◽  
Vol 20 (1) ◽  
pp. 89-100
Author(s):  
Ayhan Esi
Keyword(s):  
Normed Space ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Basic Properties ◽  
Probabilistic Normed Spaces ◽  
Convergent Sequences

Abstract In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

scholarly journals Statistical convergence of double sequences on probabilistic normed spaces defined by $[ V, \lambda, \mu ]$-summability

2014 ◽  
Vol 33 (2) ◽  
pp. 59-67
Author(s):  
Pankaj Kumar ◽  
S. S. Bhatia ◽  
Vijay Kumar
Keyword(s):  
Statistical Convergence ◽  
Convergence Criteria ◽  
Double Sequences ◽  
Normed Spaces ◽  
Real Numbers ◽  
Positive Real ◽  
Probabilistic Normed Spaces

In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$  such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in these spaces.

scholarly journals Compact Operators Defined on2-Normed and2-Probabilistic Normed Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Fatemeh Lael ◽  
Kourosh Nourouzi
Keyword(s):  
Compact Operators ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces ◽  
Main Ideas

The compact operators defined on2-normed spaces are investigated, and then the main ideas are generalized to operators defined on2-probabilistic normed spaces.

scholarly journals Some remarks on functions with values in probabilistic normed spaces

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
Ioan Goleţ
Keyword(s):  
Normed Space ◽  
Topological Properties ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Random Functions ◽  
New Class ◽  
Probabilistic Normed Spaces ◽  
Special Cases ◽  
Probabilistic Norm

AbstractIn this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.

scholarly journals λ-statistical convergence in n-normed spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 141-153 ◽  
Author(s):  
Bipan Hazarika ◽  
Ekrem Savaş
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Inclusion Relations ◽  
Convergent Sequences

Abstract In this paper, we introduce the concept of λ-statistical convergence in n-normed spaces. Some inclusion relations between the sets of statistically convergent and λ-statistically convergent sequences are established. We find its relations to statistical convergence, (C,1)-summability and strong (V, λ)-summability in n-normed spaces

Probabilistic Normed Spaces

10.1142/p944 ◽  
2014 ◽  
Author(s):  
Bernardo Lafuerza Guillen ◽  
Panackal Harikrishnan
Keyword(s):  
Normed Spaces ◽  
Probabilistic Normed Spaces
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