Some extensions of a certain integral
transform to a quotient space
of generalized functions

Al‐Omari, Shrideh; Al-Omari, J. F. M.

doi:10.1515/math-2015-0075

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…42 In particular, its suppression in macrophages has been shown to reduce the cellular production of reactive oxygen species, which play a crucial role in the perpetuation of pain and inflammation. 43 Therefore, through binding to its receptor on immune cells and possibly on peripheral nerve endings could the hydromorphone mitigate the activities of co-localized TRPV1 receptors to produce analgesia within the inflamed joint. However, as the therapeutic data suggests, the 1-day post-dosing analgesic efficacy of P-HMP is minimal, since HMP may have been entirely cleaved from the prodrug and metabolized by this time.…”

Section: Discussionmentioning

confidence: 99%

The Development of a Macromolecular Analgesic for Arthritic Pain

et al. 2019

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The addictive potential of clinically-used opioids due to their direct action on the dopaminergic reward system in the brain has limited their application. In an attempt to reduce negative side effects as well as to improve the overall effectiveness of these analgesics, we have designed, synthesized, and evaluated an N-(2-hydroxypropyl)methacrylamide (HPMA)-based macromolecular prodrug of hydromorphone (HMP), a commonly used opioid. To this end, P-HMP was synthesized via RAFT polymerization and a subsequent polymer analogous reaction. Its interaction with inflammatory cells in arthritic joints was evaluated in vitro using a RAW264.7 cell culture, and subsequent confocal microscopy analysis confirmed that P-HMP could be internalized by the cells via endocytosis. In vivo imaging studies indicated that the prodrug can passively target to the arthritic joint after systemic administration in a rodent model of monoarticular adjuvantinduced arthritis (MAA). The inflammatory pain-alleviating properties of the prodrug were assessed in MAA rats using the incapacitance test, and were observed to be similar to doseequivalent HMP. Analgesia through mechanisms at the spinal cord level was further measured using the tail flick test and it was determined that the prodrug significantly reduced spinal cord analgesia versus free HMP, further validating the peripheral restriction of the macromolecular prodrug. Immunohistochemical analysis of cellular uptake of the P-HMP within the MAA knee joint proved the internalization of the prodrug by phagocytic synoviocytes, co-localized with HMP's target receptor as well as with pain-modulating ion channels. Therefore, it can be concluded that the novel inflammation-targeting polymeric prodrug of HMP (P-HMP) has the potential to be developed as an effective and safe analgesic agent for musculoskeletal pain.

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Section: Discussionmentioning

confidence: 99%

The Development of a Macromolecular Analgesic for Arthritic Pain

et al. 2019

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“…In what follows, we construct the Boehmian spaces B 1 ≈ B(L 1 (R + ), (C ∞ (R + ), , ), ) and B 2 ≈ B(L 1 (R 2 + ), (C ∞ (R + ), , ), ⊕) with the products (to act as * ) and ⊕ (to act as ) that seem to comply with the delta sequences and the operator M α,k . We refer to [7,14,15,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] for an outright description and full details of abstract constructions of various Boehmian spaces and transform operators.…”

Section: The Spaces B 1 and Bmentioning

confidence: 99%

Certain fundamental properties of generalized natural transform in generalized spaces

Al‐Omari

Aracı

2021

Adv Differ Equ

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This paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

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“…For the construction of the Boehmian spaces, readers are to be familiar with the abstract construction of the Boehmian space. Otherwise, they may refer to [8][9][10][11][12][13][14][15][16]. Here, we make use of the following convolution products.…”

Section: Boehmian Spacesmentioning

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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Some extensions of a certain integral transform to a quotient space of generalized functions

Abstract: Abstract:In this paper, we establish certain spaces of generalized functions for a class of " s 2;1 transforms. We give the definition and derive certain properties of the extended "

Cited by 6 publications

References 21 publications

The Development of a Macromolecular Analgesic for Arthritic Pain

The Development of a Macromolecular Analgesic for Arthritic Pain

Certain fundamental properties of generalized natural transform in generalized spaces

A New Version of the Generalized Krätzel–Fox Integral Operators

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