{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:47:02Z","timestamp":1760230022091,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T00:00:00Z","timestamp":1657238400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Taif University","award":["TURSP-2020\/207"],"award-info":[{"award-number":["TURSP-2020\/207"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The purpose of this paper is to define new classes of analytic functions by amalgamating the concepts of q-calculus, Janowski type functions and (x,y)-symmetrical functions. We use the technique of convolution and quantum calculus to investigate the convolution conditions which will be used as a supporting result for further investigation in our work, we deduce the sufficient conditions, Po\u00b4lya-Schoenberg theorem and the application. Finally motivated by definition of the neighborhood, we give analogous definition of neighborhood for the classes S\u02dcqx,y(\u03b1,\u03b2) and K\u02dcqx,y(\u03b1,\u03b2), and then investigate the related neighborhood results, which are also pointed out.<\/jats:p>","DOI":"10.3390\/sym14071406","type":"journal-article","created":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T00:06:21Z","timestamp":1657497981000},"page":"1406","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Convolution Properties of q-Janowski-Type Functions Associated with (x,y)-Symmetrical Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4759-5449","authenticated-orcid":false,"given":"Fuad","family":"Alsarari","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Sciences College, Taibah University, P.O. Box 46421, Yanbu 41911, Saudi Arabia"}]},{"given":"Samirah","family":"Alzahrani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"297","DOI":"10.4064\/ap-28-3-297-326","article-title":"Some extremal problems for certain families of analytic functions","volume":"28","author":"Janowski","year":"1973","journal-title":"Ann. Pol. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.21136\/MB.1995.125897","article-title":"On (j,k)-symmetrical functions","volume":"120","author":"Liczberski","year":"1995","journal-title":"Math. Bohemca"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1080\/16583655.2019.1665487","article-title":"On Janowski functions associated with (n,m)-symmetrical functions","volume":"13","author":"Latha","year":"2019","journal-title":"J. Taibah Univ. Sci."},{"key":"ref_4","first-page":"10","article-title":"A note on starlike functions associated with symmetric points","volume":"24","author":"Latha","year":"2018","journal-title":"Afr. Mat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1017\/S0080456800002751","article-title":"On q-functions and a certain difference operator","volume":"46","author":"Jackson","year":"1909","journal-title":"Trans. R. Soc. Edinb."},{"key":"ref_6","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Q. J. Pure Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Srivastava, M., Tahir, M., Khan, B., Ahmad, Z., and Khan, N. (2019). Some general classes of q-starlike functions associated with the Janowski functions. Symmetry, 11.","DOI":"10.3390\/sym11020292"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Naeem, M., Hussain, S., Khan, S., Mahmood, T., Darus, M., and Shareef, Z. (2020). Janowski type q-convex and qclose-to-convex functions associated with q-conic domain. Mathematics, 8.","DOI":"10.3390\/math8030440"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s10476-017-0206-5","article-title":"On a class of analytic functions related to conic domains involving q-calculus","volume":"43","author":"Govindaraj","year":"2017","journal-title":"Anal. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8162182","DOI":"10.1155\/2022\/8162182","article-title":"Applications of q-Derivative Operator to the Subclass of Bi-Univalent Functions Involving-Chebyshev Polynomials","volume":"2022","author":"Khan","year":"2022","journal-title":"J. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s40995-019-00815-0","article-title":"Operators of Basic (or q-) Calculus and Fractional q-Calculus and Their Applications in Geometric Function Theory of Complex Analysis","volume":"44","author":"Srivastava","year":"2020","journal-title":"Iran. Sci. Technol. Trans. Sci."},{"key":"ref_12","first-page":"195","article-title":"A few results on generalized Janowski type functions associated with (j,k)-symmetrical functions","volume":"8","author":"Frasin","year":"2016","journal-title":"Acta Univ. Sapientiae Math."},{"key":"ref_13","first-page":"389","article-title":"A few results on Janowski functions associated with k-symmetric points","volume":"25","author":"Latha","year":"2017","journal-title":"Korean J. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"72","DOI":"10.2969\/jmsj\/01110072","article-title":"On a certain univalent mapping","volume":"11","author":"Sakaguchi","year":"1959","journal-title":"J. Math. Soc. Jpn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"15","DOI":"10.14492\/hokmj\/1498788094","article-title":"A generalization of starlike functions of order alpha","volume":"46","author":"Agrawal","year":"2017","journal-title":"Hokkaido Math. J."},{"key":"ref_16","first-page":"77","article-title":"A generalization of starlike functions","volume":"14","author":"Mourad","year":"1990","journal-title":"Complex Var. Theory Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"374","DOI":"10.2307\/1968451","article-title":"On the theory of univalent functions","volume":"37","author":"Robertson","year":"1936","journal-title":"Ann. Math."},{"key":"ref_18","first-page":"1","article-title":"Uber Uber die konforme abbildung sterngebieten","volume":"63","author":"Nevanlinna","year":"1920","journal-title":"Over-Sikt Av Fin.-Vetensk. Soc. Forh."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1090\/S0002-9939-1957-0086879-9","article-title":"Univalent functions and nonanalytic curves","volume":"8","author":"Goodman","year":"1975","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1090\/S0002-9939-1981-0601721-6","article-title":"Neighborhoods of univalent functions","volume":"81","author":"Ruscheweyh","year":"1981","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF02566116","article-title":"Hadamard products of Schlicht functions and the Polya-Schoenberg conjecture","volume":"48","author":"Ruscheweyh","year":"1979","journal-title":"Comment. Math. Helv."},{"key":"ref_22","first-page":"777","article-title":"Convolution conditions for certain classes of analytic functions","volume":"15","author":"Ganesan","year":"1984","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF01215069","article-title":"Convolution conditions for convexity, starlikeness and spiral-likeness","volume":"162","author":"Silverman","year":"1978","journal-title":"Math. 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