In this paper, we present some inequalities involving k-gamma and k-beta functions via some classical inequalities, like Chebyshev's inequality for synchronous (asynchronous) mappings, Grüss', and Ostrowski's inequality. Also, we give applications of k-beta function in probability distributions. Most of the inequalities produced in this paper are the k-analogs of existing results. If k = 1,we have the classical one. [ABSTRACT FROM AUTHOR]
In this paper, we obtain an inequality for the normalized Casorati curvature of slant submanifolds in quaternionic space forms by using T Oprea's optimization method. [ABSTRACT FROM AUTHOR]