Research Article PropertiesofCertainClassesofHolomorphicFunctionsRelatedto Strongly Janowski Type Function Bushra Kanwal , 1 Khalida Inayat Noor , 1 and Saqib Hussain 2 1 Mathematics Department, COMSATS University, Park Road, Islamabad, Pakistan 2 Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Abbottabad, Pakistan Correspondence should be addressed to Bushra Kanwal; bushrakanwal27pk@gmail.com Received 19 August 2021; Accepted 15 October 2021; Published 8 November 2021 AcademicEditor:TuncerAcar Copyright©2021BushraKanwaletal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Mostsubclassesofunivalentfunctionsarecharacterizedwithfunctionsthatmapopenunitdisc ∇ ontotheright-halfplane.is concept was later modified in the literature with those mappings that conformally map ∇ onto a circular domain. Many re- searcherswereinspiredwiththismodification,andassuch,severalarticleswerewritteninthisdirection.Onthisnote,wefurther modifythisideabyrelatingcertainsubclassesofunivalentfunctionswiththosethatmap ∇ ontoasectorinthecirculardomain.As aresult,conditionsforunivalence,radiusresults,growthrate,andseveralinclusionrelationsareobtainedforthesenovelclasses. Overall, many consequences of findings show the validity of our investigation. 1. Introduction Let A be the class of normalized analytic functions in the open unit disc ∇ � z ∈ C: |z| < 1 { } of the form g(z)� z +  ∞ n�2 b n z n , (1) where g(0)� 0 and g ′ (0)� 1. Let f(z)� z +  ∞ n�2 a n z n and g(z)� z +  ∞ n�2 b n z n be two analytic functions in A. en, f(z) is said to be sub- ordinate to g(z), denoted by f(z)≺g(z), if there exist a Schwarz function υ(z) in A, under the conditions υ(0)� 0 and |υ(z)| < 1, such that f(z)� g(υ(z)). Let S denotethesubclassof A ofunivalentfunctionsin ∇ and C, S ∗ ,and K represent the usual subclasses of S thatare convex, star-like, and close to convex in ∇, respectively. A numberofclassesrelatedwithstronglystar-likeandstrongly convex functions have been studied; for details, see [1–6]. eJanwoski-typefunctionhasbeendefinedandstudiedin [7].Here,inthisstudy,wewilldefinestronglyJanowski-type functionandwilldiscusssomenovelclassesinrelationwith this function. e strongly Janowski-type function is defined as φ α (a, b; z)� 1 + az 1 + bz   α , (2) where − 1 ≤ b < a ≤ 1and0 < α ≤ 1. It is easy to see that this function is univalent and convex in the unit disc ∇. Definition 1. Let ζ (z)� 1 +  ∞ n�1 d n z n , (3) be analytic in ∇ such that ζ (0)� 1. en, ζ (z) ∈ P α [a, b] if and only if ζ (z) ≺ φ α (a, b; z). (4) Definition 2. Let g(z)� z +  ∞ n�2 b n z n ∈ A. en, g(z) ∈ S ∗ (α) [a, b] if and only if zg ′ (z) g(z) ≺φ α (a, b; z), (5) Hindawi Journal of Mathematics Volume 2021, Article ID 1806174, 9 pages https://doi.org/10.1155/2021/1806174