TY - JOUR ID - 109815 TI - Some classes of Probabilistic Inner product spaces and related inequalities JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Harikrishnan, Panackal AU - Lafuerza Guillen, Bernardo AD - Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India. AD - Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain. Y1 - 2020 PY - 2020 VL - 6 IS - 2 SP - 180 EP - 192 KW - Probabilistic normed spaces KW - $t$-norm KW - $t$-conorm DO - 10.22034/kjm.2020.109815 N2 - 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. UR - https://www.kjm-math.org/article_109815.html L1 - https://www.kjm-math.org/article_109815_64d0951ded0a74c231310779685b3daa.pdf ER -