Differential equation and inequalities of the generalized k-Bessel functions

Abstract

In this paper, we introduce and study a generalization of the k-Bessel function of order ν given by We also indicate some representation formulae for the function introduced. Further, we show that the function is a solution of a second-order differential equation. We investigate monotonicity and log-convexity properties of the generalized k-Bessel function , particularly, in the case . We establish several inequalities, including a Turán-type inequality. We propose an open problem regarding the pattern of the zeroes of .

Radii of starlikeness and convexity of generalized Struve functions

“…So can be found the k−Beta function, the k−Zeta function and the k−Wright function. Recently, Mondal and Akel in [MA18] introduced and studied a generalization of the k−Bessel function of order ν. And also, they investigated monotonicity and log-convexity properties of the generalized k−Bessel function k W ν,c .…”

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

“…where J υ ðzÞ is the Bessel function of the first kind of order υ defined by (see, e.g., [38,41,43])…”

On monotonic and logarithmic concavity properties of generalized $k$-Bessel function

“…Comprehensive information about the log-concavity and the log-convexity properties can be found in [13] and its references. In this study, motivated by the some earlier results which are given in [14,15], our main aim is to present some monotonic and log-concavity properties of generalized k-Bessel functions. Moreover, we give some specific examples regarding our obtained result by using the relationships between Bessel-type functions and elementary trigonometric and hyperbolic functions.…”

“…In this paper, we are considering the generalized k-Bessel function defined by the following series representation (see [14]):…”