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We denote by  Open image in new window  and  Open image in new window  the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function  Open image in new window ,  Open image in new window , in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector (1984), we establish new inequalities for  Open image in new window . The results are based on the recurrence relations for  Open image in new window  and  Open image in new window  and the Turán-type inequalities for such functions. Similar investigations are developed to establish new inequalities for  Open image in new window .

Some Inequalities for Modified Bessel Functions