On a Class of Starlike Functions Associated with a Bean Shaped domain

In this paper, we introduce and explore a new class of starlike functions, denoted as S^*_B , comprising normalized univalent analytic functions f that satisfy the condition zf'(z)/f(z) √1+ z=:B(z) , where B(z) denotes a mapping from the unit disk onto a bean-shaped domain. Our investigation is focused on elucidating the characteristic properties of both B(z) and the functions within S^*_B . We establish precise conditions under which the subordination ψ (p(z),zp'(z);z) √1+ (z) implies p(z) ((1+A z)/(1+B z))^γ , where ψ (p(z),zp'(z);z) takes the form either of (1-α )p(z)+α p²(z)+β zp'(z)/pᵏ(z) or (p(z))^δ +β zp'(z)/(p(z))ᵏ . Furthermore, we establish inclusion relations for S^*_B and provide estimations for sharp radii constants pertaining to S^*_B .