Modified Dini functions: monotonicity patterns and functional inequalities

Abstract

Abstract. We deduce some new functional inequalities, like Turán type inequalities, Redheffer type inequalities, and a Mittag-Leffler expansion for a special combination of modified Bessel functions of the first kind, called modified Dini functions. Moreover, we show the complete monotonicity of a quotient of modified Dini functions by involving a new continuous infinitely divisible probability distribution. The key tool in our proofs is a recently developed infinite product representation for a special combination of Bessel functions of the first kind, which was very useful in determining the radius of convexity of some normalized Bessel functions of the first kind.

Cross-product of Bessel functions: Monotonicity patterns and functional inequalities

“…In this subsection, we study Redheffer type inequalities for Dini functions and cross-product of Bessel and modified Bessel functions. Motivated by the result from [22, Theorem 1], we extend and sharpen the Redheffer-type inequalities for modified Dini functions [8,Theorem 7]. Theorem 8.…”

“…For more details about Redheffer type inequalities one can refer to [10,11,22] and to the references therein. Recently in [8], Redheffer-type inequalities for modified Dini functions were studied. In this subsection, we study Redheffer type inequalities for Dini functions and cross-product of Bessel and modified Bessel functions.…”

On Geometric Properties of Normalized Hyper-Bessel Functions

“…Geometric properties of special functions such as Hypergeometric functions, Bessel functions, Struve functions, Mittag-Lefller functions, Wright functions and some other related functions is an ongoing part of research in geometric function theory. We refer for some geometric properties of these functions [2][3][4][5][6] and references therein.…”

Convexity of Integral Operators Involving Dini Functions

“…Recently Baricz et al [3] studied the close-to-convexity of Dini functions and some monotonicity properties and functional inequalities for the modified Dini function are discussed in [4]. Further some geometric properties of Dini functions are studied in [3,4,7]. Now, we consider the normalized Dini functions q υ : U → C defined as…”