In 1989, Kent and Richardson [Ordered probabilistic metric spaces, J. Austral. Math. Soc. Ser. A 46(1) (1989), 88-99, MR0966286 (90b:54022)] introduced the class of probabilistic quasi-metric spaces which offers a wider framework than that of metric spaces. The aim of this paper is to prove common fixed point theorems for single-valued and set-valued weakly compatible mappings in Menger probabi...

By using the symmetry of Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and logarithmic Sobolev for transform. Combining these inequalities, obtain new, short proof Heisenberg-type uncertainty principles in setting. Moreover, by combining Nash’s inequality, Carlson’s Sobolev’s embedding theorems transform, new inequalities involving L∞-norm. Finally, Lp-spaces, from which de...