Certain new applications of fourth-order differential inequality for close-to-convex harmonic functions

In this study, we introduce a new class RH0,γ,δ(λ,β) of normalized harmonic functions in the open unit disk △={τ∈C:|τ|<1}, satisfying a fourth-order differential inequality. We begin by showing that the recently introduced classes Rλγ,δ(β) and RH0,γ,δ(λ,β) have a one-to-one correspondence. Furthermore, we prove that every function in the class Rλγ,δ(β) is close-to-convex in the open unit disk △. We then investigate several additional properties of the class RH0,γ,δ(λ,β), including growth estimates, coefficient bounds, coefficient conditions, and closure properties under convex combinations and convolution.