A generalized Meijer transformation

Rao, Gautham; Debnath, Lokenath

doi:10.1155/s0161171285000370

Cited by 8 publications

(4 citation statements)

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“…The integral transformation (1) then becomes the Meijer transformation K ν . Several authors have studied this integral transformation and its variants (see, for example, [5,6] and [7]).…”

Section: Introductionmentioning

confidence: 99%

Certain inequalities for the modified Bessel-type function

Luo

Raina

2019

J Inequal Appl

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We establish some new inequalities for the modified Bessel-type function λ (β) ν,σ (x) studied by Glaeske et al. [in J. Comput. Appl. Math. 118(1-2):151-168, 2000] as the kernel of an integral transformation that modifies Krätzel's integral transformation. The inequalities obtained are closely related to the generalized Hurwitz-Lerch zeta function and complementary incomplete gamma function. We also deduce some useful inequalities for the modified Bessel function of the second kind K ν (x) and Mills' ratio M(x) as worthwhile applications of our main results.

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“…The integral transformation (1) then becomes the Meijer transformation K ν . Several authors have studied this integral transformation and its variants (see, for example, [5,6] and [7]).…”

Section: Introductionmentioning

confidence: 99%

Certain inequalities for the modified Bessel-type function

Luo

Raina

2019

J Inequal Appl

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“…However, the investigations of the Krätzel integral operators are continued by obtaining Tauberian and Abelian theorems and some related inversion formulas in the classical theory. Later in [7], Rao-Debnath have discussed the Krätzel integral on a certain space of distributions based on the kernel method of extension. Here, we give a revised version of the generalized Krätzel integral discussed by Al-Omari and Kilicman [8,9] in terms of the generality and clearance of results.…”

Section: Introductionmentioning

confidence: 99%

A New Version of the Generalized Krätzel–Fox Integral Operators

et al. 2018

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This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and b > 0 , the Fréchet space H a , b of testing functions has been identified as a subspace of certain Boehmian spaces. To establish the Boehmian spaces, two convolution products and some related axioms are established. The generalized variant of the cited Krätzel-Fox integral operator is well defined and is the operator between the Boehmian spaces. A generalized convolution theorem has also been given.

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“…for ∈ N and Re V > −1+(1/ ), > 0. The ( ) V transform was extended to generalized functions in [3] and to distributions in [4]. By ( ), we denote the space of equivalence classes of measurable functions : → R such that…”

Section: Introductionmentioning

confidence: 99%