International Journal of Applied Mathematics and Machine Learning
CONES IN COMPLETE RANDOM NORMED MODULES[1] T. X. Guo and Y. J. Yang, Ekeland’s variational principle for an
function on a complete random metric space,
Journal of Mathematical Analysis and Applications 389(1) (2012),
1-14.
DOI: https://doi.org/10.1016/j.jmaa.2011.11.025
[2] R. R. Phelps, Support cones in Banach spaces and their
applications, Advances in Mathematics 13(1) (1974), 1-19.
DOI: https://doi.org/10.1016/0001-8708(74)90062-0
[3] N. Dunford and J. T. Schwartz, Linear Operators, Vol. I,
Interscience, New York, 1957.
[4] T. X. Guo, Some basic theories of random normed linear spaces and
random inner product spaces, Acta Analysis Functionalis Applicata 1(2)
(1999), 160-184.
[5] T. X. Guo, Survey of recent developments of random metric theory
and its applications in China (II), Acta Analysis Functionalis
Applicata 3(3) (2001), 208-230.
[6] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier,
New York, 1983; Dover Publications, New York, 2005.
[7] C. Alsina, B. Schweizer and A. Sklar, Continuity property of
probabilistic norms, Journal of Mathematical Analysis and Applications
208(2) (1997), 446-452.
DOI: https://doi.org/10.1006/jmaa.1997.5333
[8] B. Lafuerza-Guillén, J. A. Rodriguez-Lallena and C. Sempi, A
study of boundedness in probabilistic normed spaces, Journal of
Mathematical Analysis and Applications 232(1) (1999), 183-196.
DOI: https://doi.org/10.1006/jmaa.1998.6261
[9] B. Lafuerza-Guillén and C. Sempi, Probabilistic norms and
convergence of random variables, Journal of Mathematical Analysis and
Applications 280(1) (2003), 9-16.
DOI: https://doi.org/10.1016/S0022-247X(02)00577-2
[10] B. Lafuerza-Guillén, C. Sempi and G. X. Zhang, A study of
boundedness in probabilistic normed spaces, Nonlinear Analysis:
Theory, Methods & Applications 73(5) (2010), 1127-1135.
DOI: https://doi.org/10.1016/j.na.2009.12.037
[11] D. Filipović, M. Kupper and N. Vogelpoth, Separation and duality
in locally 
modules, Journal of Functional Analysis 256(12)
(2009), 3996-4029.
DOI: https://doi.org/10.1016/j.jfa.2008.11.015
[12] T. X. Guo, Relations between some basic results derived from two
kinds of topologies for a random locally convex module, Journal of
Functional Analysis 258(9) (2010), 3024-3047.
DOI: https://doi.org/10.1016/j.jfa.2010.02.002
[13] T. X. Guo and G. Shi, The algebraic structure of finitely
generated 
and the Helly theorem in random normed modules,
Journal of Mathematical Analysis and Applications 381(2) (2011),
833-842.
DOI: https://doi.org/10.1016/j.jmaa.2011.03.069
