{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T04:17:52Z","timestamp":1766377072554,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:00:00Z","timestamp":1636502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Symmetry","award":["?"],"award-info":[{"award-number":["?"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently in the paper [Mediterr. J. Math.\u00a02016, 13, 1535\u20131553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the S\u01cel\u01cegean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz\u2013Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.<\/jats:p>","DOI":"10.3390\/sym13112141","type":"journal-article","created":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T23:07:21Z","timestamp":1636672041000},"page":"2141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On a Generalized Convolution Operator"],"prefix":"10.3390","volume":"13","author":[{"given":"Poonam","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ravinder Krishna","family":"Raina","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Technology & Engineering, M.P. University of Agriculture and Technology, Udaipur 313002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1204-2286","authenticated-orcid":false,"given":"Janusz","family":"Sok\u00f3\u0142","sequence":"additional","affiliation":[{"name":"College of Natural Sciences, University of Rzesz\u00f3w, Ul. Prof. Pigonia 1, 35-310 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,10]]},"reference":[{"key":"ref_1","first-page":"37","article-title":"Subordination properties of univalent functions involving a new class of operators","volume":"2","author":"Raina","year":"2014","journal-title":"Electron. J. Math. Anal. 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Simon Stevin"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1007\/s00009-015-0588-1","article-title":"On the convolution of a finite number of analytic functions involving a generalized Srivastava-Attiya operator","volume":"13","author":"Sharma","year":"2016","journal-title":"Mediterr. J. Math."},{"key":"ref_28","first-page":"111","article-title":"Certain subordination results on the convolution of analytic functions","volume":"37","author":"Sharma","year":"2014","journal-title":"J. Math. Appl."},{"key":"ref_29","first-page":"121","article-title":"The convexity of Hadamard product of three functions","volume":"29","year":"2007","journal-title":"J. Math. 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