Research Article Starlikeness Associated with Tangent Hyperbolic Function Huo Tang, 1 Muhammad Arif , 2 Khalil Ullah, 2 Nazar Khan , 3 Mirajul Haq, 2 and Bilal Khan 4 1 School of Mathematics and Computer Sciences, Chifeng University, Chifeng, 024000 Inner Mongolia, China 2 Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan 3 Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan 4 School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China Correspondence should be addressed to Nazar Khan; nazarmaths@gmail.com Received 18 March 2022; Accepted 20 April 2022; Published 20 May 2022 Academic Editor: Adel A. Attiya Copyright © 2022 Huo Tang et al. This 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. The primary objective of this study is to establish a class of starlike functions (symmetric under rotation) that are related to a tangent hyperbolic. Integral preserving properties along with the sufficiency criteria involving coefficients are investigated for the same class. Differential subordinations problems, which are linked to Janowski and tangent hyperbolic functions, are also discussed. We also utilize these findings to find sufficient conditions for the starlike functions. 1. Introduction and Motivations The purpose of this portion is to provide certain fundamental ideas in geometric function theory that will assist in the understanding of our results. In this respect, we start by defining the most fundamental class A , which contains func- tions that are holomorphic or regular or analytic in the subset D = fz : jzj <1g of the complex numbers ℂ, as follows A = g : g is regular in D with gz ðÞ = z + 〠 ∞ n=2 a n z n ( ) : ð1Þ Also, the subset set A ⊂ S comprises all normalised univalent functions in D. For the given functions g 1 , g 2 ∈ A , we say that g 1 is subordinate to g 2 , written appropri- ately as g 1 ≺ g 2 , if there exist a Schwarz function w, which is holomorphic in D with w 0 ðÞ = 0 and wz ðÞ j j < 1, ð2Þ so that g 1 z ðÞ = g 2 wz ðÞ ð Þ, z ∈ D ð Þ: ð3Þ Second, if g 2 in D is univalent, then, the following equiv- alence holds true: g 1 ≺ g 2 ⟸ g 1 0 ðÞ = g 2 0 ðÞ and g 1 D ð Þ ⊂ g 2 D ð Þ: ð4Þ In the analysis of holomorphic functions, image domains are extremely important. Based on the geometry of image domains, holomorphic functions are divided into various classes. Ma and Minda [1] proposed an analytic function ϕ ðReϕ > 0inDÞ in 1992, which is normalised by representa- tions ϕð0Þ =1 and ϕ ′ ð0Þ >0. Also, the region ϕðDÞ is a star-shaped about 1 and is symmetric on the real line axis. Particularly, (i) If we take ϕ z ðÞ = 1+ Az 1+ Bz −1 ≦ B < A ≦ 1 ð Þ, ð5Þ then, we achieve the class given by S ∗ A, B ½  ≡ S ∗ 1+ Az 1+ Bz   , ð6Þ Hindawi Journal of Function Spaces Volume 2022, Article ID 8379847, 14 pages https://doi.org/10.1155/2022/8379847