{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:28:09Z","timestamp":1760146089851,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T00:00:00Z","timestamp":1727827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution theorems are utilized to accomplish q-equivalence classes of generalized distributions called q-Boehmians. Consequently, the q-gamma operators are therefore extended to the generalized spaces and performed to coincide with the classical integral operator. Further, the generalized q-gamma integral is shown to be linear, sequentially continuous and continuous with respect to some involved convergence equipped with the generalized spaces.<\/jats:p>","DOI":"10.3390\/sym16101294","type":"journal-article","created":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T06:27:31Z","timestamp":1727850451000},"page":"1294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Notes on q-Gamma Operators and Their Extension to Classes of Generalized Distributions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8955-5552","authenticated-orcid":false,"given":"Shrideh","family":"Al-Omari","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 11134, Jordan"},{"name":"Jadara University Research Center, Jadara University, Irbid 21110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3742-6178","authenticated-orcid":false,"given":"Wael","family":"Salameh","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7761-4196","authenticated-orcid":false,"given":"Sharifah","family":"Alhazmi","sequence":"additional","affiliation":[{"name":"Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Q. 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