Strong and weak convergences in 2-probabilistic normed spaces

Open Access

Original research article

Author(s):

Panackal Harikrishnan^a, Bernardo Lafuerca Guillen^b, Ravi P. Agarwal^c, Hamid Reza Morad^d

^aDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India
^bDepartamento de Matemática Aplicada y Estadística, Universidad de Almería, Almería, Spain
^cDepartment of Mathematics, Texas A & M University–Kingsville, Texas, USA
^dFaculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran.

Advances in the Theory of Nonlinear Analysis and its Applications 5 (4), 454.

Received: April 4, 2021

Accepted: June 15, 2021

Published: June 17, 2021

Abstract

In this paper, we have introduced the notions of strong and weak convergences in 2-probabilistic normed spaces (2-PN spaces) and established some of their properties. Later, we have defined the strong and weak boundedness of a linear map between two 2-PN spaces and proved a necessary and sufficient condition for the linear map between two 2-PN spaces to be strongly and weakly bounded.

Keywords: Menger’s probabilistic normed spaces; Linear 2-normed spaces; Triangle functions; t-norms.

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APA Style

Harikrishnan, P., Guillen, B. L., Agawral, R. P., & Moradi, H. R. (2021). Strong and weak convergences in 2-probabilistic normed spaces. Advances in the Theory of Nonlinear Analysis and its Applications , 5 (4), 454.