Corpus ID: 235765463

New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality

@inproceedings{cCakmak2021NewSO,
  title={New subclass of the class of close-to-convex harmonic mappings defined by a third-order differential inequality},
  author={Serkan cCakmak and Elif Yacsar and Sibel Yalccin},
  year={2021}
}
In this paper, we introduce a new subclass of harmonic functions f = s+ t in the open unit disk U = {z ∈ C : |z| < 1} satisfying Re [ γs′(z) + δzs′′(z) + ( δ−γ 2 ) z2s′′′ (z)− λ ] > ∣∣γt′(z) + δzt′′(z) + ( δ−γ 2 ) z2t′′′ (z) ∣∣ , where 0 ≤ λ < γ ≤ δ, z ∈ U . We determine several properties of this class such as close-to-convexity, coefficient bounds, and growth estimates. We also prove that this class is closed under convex combination and convolution of its members. Furthermore, we investigate… Expand

References

SHOWING 1-10 OF 24 REFERENCES
New subclasses of the class of close-to-convex functions
In this paper we introduce new subclasses of the class of closeto-convex functions. We call a regular function Az) an alpha-close-to-convex function if (f(z)f'(z)/z) # 0 for z in E and if for someExpand
Close-to-convexity of a class of harmonic mappings defined by a third-orderdifferential inequality
Abstract: In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality and we investigate several properties of this classExpand
Stable geometric properties of analytic and harmonic functions
Abstract Given any sense preserving harmonic mapping f=h+ḡ in the unit disk, we prove that for all |λ|=1 the functions fλ=h+λḡ are univalent (resp. close-to-convex, starlike, or convex) if and onlyExpand
Some properties for a class of analytic functions defined by a higher-order differential inequality
for some λ (λ < p!{α+(p−j)β+(p−j)(p−j−1)(β−α)/2}/(p−j)!) and j = 0, 1, ..., p , where p+1−j+2α/(β−α) > 0 or α = β = 1 . The extreme points of Bp(α, β, λ; j) are determined and various sharpExpand
Convolution properties of a class of starlike functions
Let R denote the class of functions f(z) = z + a2z2 +* that are analytic in the unit disc E = {z: Izi K 1 } and satisfy the condition Re(f'(z) + zf"(z)) > 0, z E E. It is known that R is a subclassExpand
A subclass of close-to-convex harmonic mappings
A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem,Expand
Hadamard Products of Convex Harmonic Mappings
Functions f in the class $ K_H $ are convex, univalent, harmonic, and sense preserving in the unit disk. Such functions can be expressed as $ f = h + \overline {g} $ where h and g are analyticExpand
Convolutions of planar harmonic convex mappings
Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convexExpand
Inclusion properties for a class of analytic functions defined by a second-order differential inequality
For $$\beta <1$$β<1, and $$\alpha \ge \gamma \ge 0,$$α≥γ≥0, let $$\mathcal {W}_{\beta }(\alpha ,\gamma )$$Wβ(α,γ) consist of normalized analytic functions f in the unit disk satisfyingExpand
Construction of subclasses of univalent harmonic mappings
TLDR
The notion of harmonic Alexander integral operator is introduced and the radius of convexity for certain families of harmonic functions is determined. Expand
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