Holder Inequalities for a subclass of univalent functions involving Dziok-Srivastava Operator

Abstract

In this paper, we introduce a new subclasses of univalent functions defined in the open unit disc involving DziokSrivastava Operator . The results on modified Hadamard product ,Holder inequalities and closure properties under integral transforms are discussed.

Holder and Integral Means Inequalities for a Certain Subclass of Analytic Functions Based on Caputo's Fractional Operator

“…Followed by Nishiwaki et al [11] and Murugusundaramoorthy et al [10] in this section we study some results of Holder type inequalities for f ∈ T J η µ (α, β, γ, A, B). Now we recall the generalisation of the convolution due to Cho et al [5] as given below…”

Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

“…Following the works of Murugusundaramoorthy et al [12,13], we discuss integral transformation results for a function f (z) ∈ SI m (ξ, η, δ). Definition 2.…”

“…which gives the Komatu operator (for details, see [13]). We now show that the class SI m (ξ, η, δ) is closed under V σ ( f )(z).…”

“…Following the work of Murugusundaramoorthy et al [13], we determine the convolution properties for functions belonging to the class SI m (ξ, η, δ).…”

Holder's Inequalities for a New Class of P-Valent Analytic Functions

“…We note that: (i) For p = m = 1, λ = 0 and = 0, we have DF m,p,δ λ, ,γ (α, β, A, B) = HF δ γ (α, β, A, B) (see Murugusundaramoothy et al [11]); (ii) For m = δ = 0, β = γ = B = 1 and A = −1, we have DF 0,p,0 λ, ,γ (α, β, A, B) = S * p (α) , for m = 0 and δ = β = γ = 1, we have DF 0,p,1 λ, ,γ (α, β, A, B) = K p (α) (see also Nishiwaki and Owa [13], with n = 1).…”