Monotonicity property of generalized and normalized Bessel functions of complex order

András, Szilárd; Baricz, Árpád

doi:10.1080/17476930902998936

Cited by 14 publications

(10 citation statements)

References 9 publications

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“…It is important to note here that the above result is related to a recent open problem from [1] concerning a subordination property of normalized Bessel functions with different parameters. Now, choosing in the above inequalities p = − 3 2 , b = c = 1 (κ = − 1 2 ) and p = − 1 2 , b = c = 1 (κ = 1 2 ), respectively, we obtain for all z ∈ D and |a| < 1 2 the following chain of implications…”

Section: Corollarymentioning

confidence: 72%

Differential Subordinations and Superordinations for Generalized Bessel Functions

Al-Kharsani

Baricz

Nisar

2016

Bulletin of the Korean Mathematical Society

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Section: Corollarymentioning

confidence: 72%

Differential Subordinations and Superordinations for Generalized Bessel Functions

Al-Kharsani

Baricz

Nisar

2016

Bulletin of the Korean Mathematical Society

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“…This author called a particular solution of the differential Equation 1 as the generalized BF of the first kind of order and also denoted by w ,b,d (z). Also it is shown that functions w ,b,d (z) have the following representation (see also previous studies [45][46][47][48][49][50][51][52][53][54][55][56] for more details):…”

Section: Introductionmentioning

confidence: 94%

Generalized Bessel functions: Theory and their applications

Khosravian-Arab

Dehghan

Eslahchi

2017

Math Methods in App Sciences

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This paper presents 2 new classes of the Bessel functions on a compact domain[0, T] as generalized-tempered Bessel functions of the first-and second-kind which are denoted by GTBFs-1 and GTBFs-2. Two special cases corresponding to the GTBFs-1 and GTBFs-2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self-adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders. KEYWORDS Bagley-Torvik equation, Bessel functions, fractional derivatives and integrals, Gaussian quadrature rules, relaxation-oscilation equation, self-adjoint operator, spectral Galerkin method, tempered fractional derivatives and integrals Math Meth Appl Sci. 2017;40:6389-6410.wileyonlinelibrary.com/journal/mma Esmaeili and Shamsi 30 were the first authors who introduced a new class of the Jacobi polynomials to solve some fractional differential equations. It is worthwhile noting that the new set, generally due to the nonpolynomial nature, is in fact, a set of orthogonal basis functions. These basis functions are also performed to solve some fractional optimal control problems and calculus of variations. [31][32][33] Later, Zayernouri and Karniadakis 34 introduced 2 new classes of Jacobi functions, which are orthogonal with respect to some suitable weight functions, as the eigenfunctions of some fractional Sturm-Liouville eigenvalue problems on [−1, 1]. They also used these basis functions to solve various fractional differential equations. (See for instance Zayernouri and Karniadakis 35-37 and other papers of the same authors. Also see Chen et al 38 and references therein.) After them, Khosravian-Arab et al 39 introduced 2 new classes of generalized Laguerre functions, which are also orthogonal with respect to some weight functions on [0, ∞).As we are aware, one of the most interesting and very practical functions which arises frequently in mathematical physics is the Bessel function(s) (BF(s)). From the historical point of view, the BFs arose in Daniel Bernoulli's investigation of the oscillations of a hanging chain, Euler's theory of the vibration of a circular membrane, and Bessel's studies of planetary motion. Recently, several applications of BFs have been discovered in physics and engineering such as propagation of waves, elasticity, fluid motion, and in many problems of potential theory and diffusion involving cylindrical symmetry. [40][41][42] Although, the BFs are usually known as the solutions of a second-order differential equation, so-called as Bessel's differential equation, which arises by the use of the separation of the variables for various problems in mathematical physics, but, in fact, there is a very close connection betw...

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“…In the case when Ω = C is a simply connected domain with Ω = h(D) for some conformal mapping h of D onto Ω. In this case the class Φ H, 1…”

Section: áRpád Baricz Erhan Deniz Murat ç Aglar and Halit Orhanmentioning

confidence: 99%

“…For further result on the transformation (1.8) of the generalized Bessel function we refer to the recent papers (see [1,2,3,4,14,15,16]), where among other things some interesting functional inequalities, integral representations, application of admissible functions, extensions of some known trigonometric inequalities, starlikeness and convexity and univalence were established. Most of these results were motivated by the research on geometric properties of Gaussian and Kummer hypergeometric functions.…”

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confidence: 99%

Differential Subordinations Involving Generalized Bessel Functions

Baricz

Deni̇z

Çağlar

et al. 2014

Bull. Malays. Math. Sci. Soc.

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In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results and we point out various known or new special cases of our main results.Comment: 15 pages, accepted in Bulletin of the Malaysian Mathematical Sciences Societ

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Monotonicity property of generalized and normalized Bessel functions of complex order

Cited by 14 publications

References 9 publications

Differential Subordinations and Superordinations for Generalized Bessel Functions

Differential Subordinations and Superordinations for Generalized Bessel Functions

Generalized Bessel functions: Theory and their applications

Differential Subordinations Involving Generalized Bessel Functions

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