On Starlike Functions Associated with a Bean Shaped Domain

In this paper, we introduce and explore a new class of starlike functions denoted by S^*B, defined as follows: S^*B=∈ A:zf'(z)/f(z) √1+z=:B(z)\. Here, B(z) represents a mapping from the unit disk onto a bean-shaped domain. Our study focuses on understanding the characteristic properties of both B(z) and the functions in S^*B. We derive sharp conditions under which ψ(p)√1+(z) implies p(z) ((1+A z)/(1+B z))^γ, where ψ(p) is defined as: {equation*} (1-α)p(z)+α p^2(z)+β zp'(z)/p^k(z) and (p(z))^δ+β zp'(z)/(p(z))^k. {equation*} Additionally, we establish inclusion relations involving S^*B and derive precise estimates for the sharp radii constants of S^*B.