eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2018-05-05 6 3 61 71 10.12691/tjant-6-3-1 TJANT2018631 article Oppenheim's Problem and Some Inequalities Involving Bessel Functions and Dunkl Kernels Frej Chouchene frej.chouchene@essths.u-sousse.tn 1 Department of Mathematics, University of Sousse, Higher School of Sciences and Technology of Hammam Sousse, 4011 Hammam Sousse, Tunisia In this paper, we establish some inequalities related to Oppenheim's problem for the real and imaginary parts of Dunkl kernels In order to prove our main results, we present some new inequalities involving Bessel functions of the first kind. Refinements of inequalities for Bessel functions are also given. http://pubs.sciepub.com/tjant/6/3/1/tjant-6-3-1.pdf Oppenheim's problem Bessel functions modified Bessel functions Dunkl kernels