(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Let SK[ P,Q;α ,β ] denote the subfamily of normalized regular functions g(ξ )=ξ +d_2ξ ^2+d_3ξ ^3+d_4ξ ^4+... in the open unit disk Δ holding the next subordination condition: equation* α g( ξ ) +β ξ g^′ ( ξ ) % α ξ +β g( ξ ) 1+[ Q+( 1-γ ) ( P-Q) ] ξ 1+Mξ , equation* where 0≤ α ,β ≤ 1, -1≤ Q<P≤ 1, 0≤ γ <1 and ξ Δ . In this article, we study some geometric properties such as convolution results, coefficient estimates, the upper bounds for the initial coefficients of the first four coefficients and the Fekete-Szegö inequalities for this subfamily.