Convex sets in probabilistic normed spaces

2008 ◽  
Vol 36 (2) ◽  
pp. 322-328 ◽  
Author(s):  
Asadollah Aghajani ◽  
Kourosh Nourouzi
Keyword(s):  
Convex Sets ◽  
Normed Spaces ◽  
Probabilistic Normed Spaces

scholarly journals Compactness and D-Boundedness in Menger’s 2-probabilistic normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1263-1272 ◽  
Author(s):  
P.K. Harikrishnan ◽  
Bernardo Guillén ◽  
K.T. Ravindran
Keyword(s):  
Normed Space ◽  
Convex Sets ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Probabilistic Normed Spaces

The idea of convex sets and various related results in 2-Probabilistic normed spaces were established in [7]. In this paper, we obtain the concepts of convex series closedness, convex series compactness, boundedness and their interrelationships in Menger?s 2-probabilistic normed space. Finally, the idea of D-Boundedness in Menger?s 2-probabilistic normed spaces and Menger?s Generalized 2-Probabilistic Normed spaces are discussed.

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.

Probabilistic Normed Spaces

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

scholarly journals Statistical Summability through de la Vallée-Poussin Mean in Probabilistic Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ayhan Esi
Keyword(s):  
Statistical Convergence ◽  
The Other ◽  
Normed Spaces ◽  
Summability Methods ◽  
Probabilistic Normed Spaces ◽  
New Type ◽  
De La Vallée Poussin

Two concepts—one of statistical convergence and the other of de la Vallée-Poussin mean—play an important role in recent research on summability theory. In this work we define a new type of summability methods and statistical completeness involving the ideas of de la Vallée-Poussin mean and statistical convergence in the framework of probabilistic normed spaces.

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