Related papers: Certain Geometric Properties of Some Bessel Functi…
This work provides formulae for the $\epsilon$-subdifferential of integral functions in the framework of complete $\sigma$-finite measure spaces and locally convex spaces. In this work we present here new formulae for this…
This paper explores the asymptotic behaviour of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence…
In the paper we show the existence of different types of peak functions in classes of $\mathbb C$-convex domains. As one of tools used in this context is a result on preserving the regularity of $\mathbb C$-convex domains under projection.
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
In this paper we consider a new nonlinear mathematical model for corneal topography formulated as two-point boudary value problem. We derive it from first physical principles and provide some mathematical analysis. The existence and…
We consider tessellations of the Euclidean $(d-1)$-sphere by $(d-2)$-dimensional great subspheres or, equivalently, tessellations of Euclidean $d$-space by hyperplanes through the origin; these we call conical tessellations. For random…
We develop a new point of view to introduce families of functions, which can be identified as generalization of the ordinary trigonometric or hyperbolic functions. They are defined using a procedure based on umbral methods, inspired to the…
In this paper we determine the Bochner measure for spherical functions on a semi-simple Lie group of rank one.
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
We compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness,…
Series involving hypergeometric functions are used to derive, extend and evaluate integrals involving the product of two Bessel functions of the first kind $J_{u}(a z)$ $J_{v}(b z)$ with order $u,v$, studied by Landau et al. The method used…
In this paper, we consider a subclass of starlike functions associated with a vertical strip domain. Several results concerned with integral representations, convolutions, and coefficient inequalities for functions belonging to this class…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
We define a q-analog of the modified Bessel and Bessel-Macdonald functions. As for the q-Bessel functions of Jackson there is a couple of functions of the both kind. They are arisen in the Harmonic analysis on quantum symmetric spaces…
The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for…
This paper deals with some radius results and inclusion relations that are established for functions in a newly defined subclass of starlike functions associated with a petal shaped domain.
We analyze a class of sublinear functionals which characterize the interior and the exterior of a convex cone in a normed linear space.