Some classes of Probabilistic Inner product spaces and related inequalities

Document Type : Original Article

Authors

Panackal Harikrishnan ¹

Bernardo Lafuerza Guillen ²

¹ Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.

² Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain.

10.22034/kjm.2020.109815

Abstract

We give a new definition for probabilistic inner product spaces, which is sufficiently general to encompass the most important class of probabilistic inner product spaces (briefly, PIP spaces). We have established certain classes of PIP spaces and especially, illustrated that how to construct a real inner product from a Menger PIP space. Finally, we have established the analogous of  Cauchy--Schwarz inequality in this general PIP spaces.

Keywords

Probabilistic normed spaces

$t$-norm

$t$-conorm

Subjects

• 46 Functional analysis

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