Tom 29 (2021): Zeszyt 2 (December 2021)

We present a sequence of sets converging, under suitable conditions and respect to the Hausdorff intuitionistic fuzzy metric, to the attractor set of certain intuitionistic fuzzy iterated function systems. For this goal, we will introduce a fuzzy version of the so called α-dense curves which have been used by the author to approximate, with arbitrarily small and controlled error, the attractor set of certain (metric) iterated function systems. In this way, we relate the above mentioned concepts of the intuitionistic fuzzy metric spaces with the α-density theory.

In this paper, we consider new subclasses 𝔗𝔖_n(µ, a, b, ℓ, τ, γ) and 𝕽_n(µ, a, b, ℓ, τ, γ) of analytic univalent functions defined by Erdelyi-Kober integral operator. We obtain coefficient inequalities, inclusion relationships involving the (n, δ)- neighborhoods, partial sums and integral mean inequalities for the functions that belongs to these classes. Also, subordinating factor sequence for the functions in the classes 𝔖_n(µ, a, b, ℓ, τ, γ) and 𝕽_n(µ, a, b, ℓ, τ, γ) are derived.

In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fejér’s inequality for convex functions and of Grüss’ type inequalities are also provided.

In this paper, we introduce and study a new class k − ŨS_s(a, c, µ, γ, t) of analytic functions in the open unit disc U with negative coefficients and obtain coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.

In this research article, making use of Erdelyi-Kober integral operator, we define a new subclass T^a,c_µ(α, β, γ, A, B) of starlike functions with negative coefficient. Various properties like coefficient estimates, neighbourhood results, integral means, partial sums and subordination results are examined for this class.

In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses D^n,ρ_Σ,δ(Φ) and F^n,α_Σ,δ(Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |a₂| and |a₃| of the bi-univalent function subclasses.

By means of Jackson’s (p, q)–derivative a new class of univalent functions based on subordination is defined. We evoke some geometric properties such as coefficient estimate, convolution preserving, convexity and radii properties of this class of functions are obtained.

In this paper we obtain the sharp Bohr radius, Bohr-Rogosinski radius, improved Bohr-radius and refined Bohr radius for the functions in the class GH¯0(γ) G_{\bar H}^0\left( \gamma \right) of Goodman-Ronning type harmonic univalent functions with negative coeffcients.

This paper deals with the class S containing functions which are analytic and univalent in the open unit disc U = {z ∈ ℂ : |z| < 1}. Functions f in S are normalized by f(0) = 0 and f′(0) = 1 and has the Taylor series expansion of the form f(z)=z+∑n=2∞anzn f\left( z \right) = z + \sum\limits_{n = 2}^\infty {{a_n}{z^n}} . In this paper we investigate on the subclass of S of close-to-convex functions denoted as C_gα(λ, δ) where function f ∈ C_gα(λ, δ) satisfies Re{ eiλzf′(z)gα(z) } {\mathop{\rm Re}\nolimits} \left\{ {{e^{i\lambda }}{{zf'\left( z \right)} \over {g\alpha \left( z \right)}}} \right\} for | λ |<π2 \left| \lambda \right| < {\pi \over 2} , cos(λ) > δ, 0 ≤ δ < 1, 0 ≤ α ≤ 1 and gα=z(1−αz)2 {g_\alpha } = {z \over {{{\left( {1 - \alpha z} \right)}^2}}} . The aim of the present paper is to find the upper bound of the Fekete-Szego functional |a₃ − µa₂²| for the class C_gα(λ, δ). The results obtained in this paper is significant in the sense that it can be used in future research in this field, particularly in solving coefficient inequalities such as the Hankel determinant problems and also the Fekete-Szego problems for other subclasses of univalent functions.

The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.