<abstract xmlns="http://www.w3.org/1999/xhtml">

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 <italic>fuzzy version</italic> of the so called <italic>α</italic>-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 <italic>α</italic>-density theory.
</abstract>

Approximating intuitionistic fuzzy fractals by densifiability techniques

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we consider new subclasses 𝔗𝔖<italic>n</italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) and 𝕽<italic>n</italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) of analytic univalent functions defined by Erdelyi-Kober integral operator. We obtain coefficient inequalities, inclusion relationships involving the (<italic>n, δ</italic>)- 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<italic>n</italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) and 𝕽<italic>n</italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) are derived.
</abstract>

On certain classes of analytic functions of Complex order defined by Erdelyi-Kober integral operator

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Integral Inequalities Related to Wirtinger’s Result

<abstract xmlns="http://www.w3.org/1999/xhtml">

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

On A Certain Subclass Of Analytic Functions Defined By Linear Operator

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this research article, making use of Erdelyi-Kober integral operator, we define a new subclass <italic>Ta,c</italic><italic>µ</italic>(<italic>α, β, γ, A, B</italic>) 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.
</abstract>

On Certain Subclass of Starlike Functions with Negative Coefficients Associated with Erdelyi-Kober Integral Operator

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses <italic>D</italic><italic>n,ρ</italic>Σ,<italic>δ</italic>(Φ) and <italic>F</italic><italic>n,α</italic>Σ,<italic>δ</italic>(Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |<italic>a</italic>2| and |<italic>a</italic>3| of the bi-univalent function subclasses.
</abstract>

Faculty of Computer and Mathematical Sciences

Universiti Teknologi MARA Sabah Branch, Kota Kinabalu Campus

New Subclasses of Bi-Univalent Functions based on the Fibonacci Numbers

<abstract xmlns="http://www.w3.org/1999/xhtml">

By means of Jackson’s (<italic>p, q</italic>)–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.
</abstract>

(<italic>p, q</italic>)–derivative on univalent functions associated with subordination structure

<abstract xmlns="http://www.w3.org/1999/xhtml">

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 <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2021-0018_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>G</mi></mrow><mover accent="true"><mi>H</mi><mo>¯</mo></mover><mn>0</mn></msubsup><mrow><mo>(</mo><mi>γ</mi><mo>)</mo></mrow></mrow></math>
<tex-math>G_{\bar H}^0\left( \gamma \right)</tex-math>
</alternatives>
</inline-formula> of Goodman-Ronning type harmonic univalent functions with negative coeffcients.
</abstract>

Bohr Radius for Goodman-Ronning Type Harmonic Univalent Functions

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper deals with the class <italic>S</italic> containing functions which are analytic and univalent in the open unit disc <italic>U</italic> = {<italic>z</italic> ∈ ℂ : |<italic>z</italic>| &lt; 1}. Functions <italic>f</italic> in <italic>S</italic> are normalized by <italic>f</italic>(0) = 0 and <italic>f</italic>′(0) = 1 and has the Taylor series expansion of the form <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2021-0019_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>z</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></munderover><mrow><msub><mrow><mi>a</mi></mrow><mi>n</mi></msub><msup><mrow><mi>z</mi></mrow><mi>n</mi></msup></mrow></mrow></math>
<tex-math>f\left( z \right) = z + \sum\limits_{n = 2}^\infty {{a_n}{z^n}}</tex-math>
</alternatives>
</inline-formula>. In this paper we investigate on the subclass of <italic>S</italic> of close-to-convex functions denoted as <italic>C</italic><italic>gα</italic>(<italic>λ, δ</italic>) where function <italic>f</italic> ∈ <italic>C</italic><italic>gα</italic>(<italic>λ, δ</italic>) satisfies <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2021-0019_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>Re</mo><mrow><mo>{</mo> <mrow><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mi>λ</mi></mrow></msup><mfrac><mrow><mi>z</mi><msup><mi>f</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow><mrow><mi>g</mi><mi>α</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></mfrac></mrow> <mo>}</mo></mrow></mrow></math>
<tex-math>{\mathop{\rm Re}\nolimits} \left\{ {{e^{i\lambda }}{{zf'\left( z \right)} \over {g\alpha \left( z \right)}}} \right\}</tex-math>
</alternatives>
</inline-formula> for <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2021-0019_eq_003.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mo>|</mo> <mi>λ</mi> <mo>|</mo></mrow><mo>&lt;</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></mrow></math>
<tex-math>\left| \lambda \right| &lt; {\pi \over 2}</tex-math>
</alternatives>
</inline-formula>, cos(<italic>λ</italic>) <italic>> δ</italic>, 0 ≤ <italic>δ &lt;</italic> 1, 0 ≤ <italic>α</italic> ≤ 1 and <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2021-0019_eq_004.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mi>α</mi></msub><mo>=</mo><mfrac><mi>z</mi><mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mi>α</mi><mi>z</mi></mrow><mo>)</mo></mrow></mrow></mrow><mn>2</mn></msup></mrow></mfrac></mrow></math>
<tex-math>{g_\alpha } = {z \over {{{\left( {1 - \alpha z} \right)}^2}}}</tex-math>
</alternatives>
</inline-formula>. The aim of the present paper is to find the upper bound of the Fekete-Szego functional |<italic>a</italic>3 − <italic>µa</italic>22| for the class <italic>C</italic>g<italic>α</italic>(<italic>λ, δ</italic>). 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.
</abstract>

Faculty of Computer and Mathematical Sciences, Department of Mathematics

The Fekete-Szego Theorem for Close-to-convex Functions Associated with The Koebe Type Function

<abstract xmlns="http://www.w3.org/1999/xhtml">

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 (<italic>cond-cdf</italic>) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated <italic>cond-cdf</italic>, 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.
</abstract>

University Djillali LIABES of Sidi Bel Abbes

Faculty of Exact Sciences, Probability and Statistics

Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship

AHEAD OF PRINT

Volume 31 (2023): Issue 2 (December 2023)

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Volume 30 (2022): Issue 2 (December 2022)

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Volume 29 (2021): Issue 2 (December 2021)

Volume 29 (2021): Issue 1 (June 2021)

Volume 28 (2020): Issue 2 (December 2020)

Volume 28 (2020): Issue 1 (June 2020)

Volume 27 (2019): Issue 2 (December 2019)

Volume 27 (2019): Issue 1 (June 2019)

General Mathematics

 Publishing House and Owner: Lucian Blaga University of Sibiu, Romania   General Mathematics publishes high quality papers on pure and applied mathematics. To be published in this journal, a paper must contain new ideas and be of interest to a wide range of readers. Survey papers are also welcome.The journal appears in 2 numbers per year and has been published since 1993.It is edited by the Department of Mathematics and Informatics of the “Lucian Blaga” University of Sibiu.  The purpose of General Mathematics is to provide an outlet for high quality original research in all areas of analysis or that having applications in economics, engineering, the life sciences, physics and statistical decision theory.  Coverage touches on a wide variety of topics, including:   Functional analysis and operator theory  Real and harmonic analysis　  Complex analysis　  Numerical analysis　  Applied mathematics　  Partial differential equations　  Dynamical systems　  Control and Optimization　  Probability　  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 