Research Article Applications of Some Generalized Janowski Meromorphic Multivalent Functions Bakhtiar Ahmad , 1 Muhammad Ghaffar Khan , 2 Maslina Darus , 3 Wali Khan Mashwani , 2 and Muhammad Arif 1 1 Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan 2 Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, Pakistan 3 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, Malaysia CorrespondenceshouldbeaddressedtoMuhammadGhaffarKhan;ghaffarkhan020@gmail.com Received 11 November 2020; Revised 2 July 2021; Accepted 15 July 2021; Published 26 July 2021 AcademicEditor:Ming-ShengLiu Copyright © 2021 Bakhtiar Ahmad et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Inthisarticle,theideasofpost-quantumcalculusandmeromorphicmultivalentfunctionsarecombinedandsomeapplicationsof thesefunctionsarediscussed.WeintroduceanewsubclassofmeromorphicmultivalentfunctionsinassociationwithJanowski domain.Weinvestigateandstudysomeusefulgeometricpropertiesofthisclassoffunctionssuchassufficiencycriteria,distortion problem, growth theorem, radii of starlikeness and convexity, convex combination, and coefficient estimates for this class. 1. Introduction and Definitions Inthisarticle,weintroduceanewsubclassofmeromorphic multivalent functions in parameter α, in post-quantum analogue. e quantum calculus (q-calculus) is the gener- alizationofclassicalcalculusbyreplacingthenotionoflimits withaparameter q.Inthefieldofgeometricfunctiontheory (GFT), the q-generalization of different classes of analytic and meromorphic functions is the current focus of various prominent researchers. Many generalizations have been made and various properties are discussed for these gen- eralizations. is motivation in the recent past is due to its numerous mathematical and physical applications. Jackson started this area of mathematics with the generalization of derivative and integral in q-analogue, which are known as q-derivativeand q-integral[1,2].elatestadvancementsin thisfieldcanbetracedtoSrivastava,whoalongwithBansal [3], investigated a certain family of q-Mittag-Leffer func- tions.AldawishandDarus[4]gaveresultsonstarlikenessof q-generalized functions. Some results such as coefficient estimates for q-starlike and q-convex functions were evaluated by Seody and Aouf [5]. Similar results for some other subclasses of q-starlike functions were evaluated by Fan et al. in [6]. Mahmood and Sok´ oł in [7] introduced a class in conical domain associated with Ruscheweyh q-differential operator and investigated its various proper- ties. Shi et al. [8] used a generalized operator in the in- troduction and study of a class of analytic functions. Wang et al. [9] gave a useful generalization of Choi–Saigo–Srivastava operator in q-analogue. For other interesting results, the reader is referred to the work pub- lished in [10, 11]. Similarly, the trend was carried to mer- omorphic functions by various researchers. Ahmad et al. [12] gave the investigation of q-analogue of meromorphic multivalentfunctionsinlemniscateofBernoullidomainand obtained some interesting results. Arif and Ahmad [13] introduced and studied q-analogue of a meromorphic multivalent operator and presented some interested results. e convex generalization of meromorphic multivalent functionsin q-analoguecanbeseenin[14].Furtherworkby AhmadandArif[15]generalizedasubclassofmeromorphic multivalent close to convex functions via a q-operator. Hindawi Journal of Mathematics Volume 2021, Article ID 6622748, 13 pages https://doi.org/10.1155/2021/6622748