<abstract>
<title style='display:none'>Abstract</title>
To approximate a function, some simpler functions are used: simpler as definitory structure (formula) and also as regularity, continuity and/or smoothness.
Any Lipschitz function is a uniformly continuous function, but conversely it not always true. We add to the usual examples some other, especially of the class of differentiable functions.
</abstract>

About uniform continuous functions which are not Lipschitz

<abstract>
<title style='display:none'>Abstract</title>
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><title style='display:none'>Abstract</title>In this paper we have introduced two new types of sets termed as 𝕀*<italic>µ</italic> sets and strongly 𝕀*<italic>µ</italic> -open sets and discussed some of its properties. The relation between similar types of sets, characterizations and some basic properties of such sets have been studied.</abstract>

𝕀*<italic>µ</italic> open sets in generalized topological spaces

Book Review: Recent Advances in Constructive Approximation Theory By: V. Gupta, T.M. Rassias, P.N. Agrawal, A.M. Acu Springer Optim. Appl. 138, Springer, Cham, 2018, DOI 10.1007/978-3-319-92165-5

<abstract>
<title style='display:none'>Abstract</title>
We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive. Futhermore, we applied our main result for finding a common solution of convex minimization problem and fixed points problem. Essentially a new approach for finding solutions of equilibrium problems and fixed point problems whith set-valued operators is provided.
</abstract>

A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we introduce a new class of generalized convex functions called (<italic>h, r</italic>)-preinvex functions, and establish some new Hermite-Hadamard type inequalities under (<italic>h, r</italic>)-preinvexity.
</abstract>

Hermite-Hadamard’s inequalities for (<italic>h, r</italic>)-preinvex functions

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we establish new iterative methods for the solution of scalar equations by using the decomposition technique given in [<xref ref-type="bibr" rid="j_gm-2023-0009_ref_016">16</xref>].
</abstract>

Iterative methods for solving scalar equations

<abstract>
<title style='display:none'>Abstract</title>
In this paper, using the method of Hicks, we prove some new related fixed point theorems for pair of mappings on two <italic>d</italic>-complete topological spaces under the suitable conditions. We also derive some related fixed point theorems from our main results. Finally, by using <italic>w</italic>-continuity, we establish a related fixed point theorem in <italic>d</italic>-complete Hausdorff topological spaces.
</abstract>

On related fixed points in two <italic>d</italic>-complete topological spaces

<abstract>
<title style='display:none'>Abstract</title>
Let 𝒜 be the class of normalized functions which are analytic in the open unit disc. Jakson <italic>q</italic>-derivative represented by convolution operator
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2023-0011_eq_001.png"/>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mi>q</mml:mi></mml:msub><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>z</mml:mi></mml:mfrac><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>★</mml:mo><mml:mfrac><mml:mi>z</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>q</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mi>z</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow> <mml:mo>}</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi>f</mml:mi><mml:mo>∈</mml:mo><mml:mi>𝒜</mml:mi><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi>q</mml:mi><mml:mo>∈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
<tex-math>{D_q}f\left( z \right) = {1 \over z}\left\{ {f\left( z \right)\star{z \over {\left( {1 - qz} \right)\left( {1z} \right)}}} \right\},\,\,\,\,f \in \mathcal{A},\,\,\,q \in \left( {0,1} \right)</tex-math>
</alternatives>
</disp-formula>
is used to introduce a unified class <italic>Mq</italic>(<italic>α, β, γ</italic>), <italic>α</italic> ≥ 0, <italic>β, γ</italic> ∈ [0, 1) and its various mapping properties are studied. For <italic>q</italic> → 1−1, <italic>β</italic> = <italic>γ</italic> = 0 and <italic>α</italic> = 1, this class reduces to the class <italic>K</italic> of close-to-convex univalent functions. A number of interesting results such as <italic>q</italic>-Bernardi integral operator and inclusion relations are included as part of this study. Applications are also pointed out as consequences of the main results.
</abstract>

On analytic functions related with <italic>q</italic>-generalized bounded Mocanu variation

<abstract>
<title style='display:none'>Abstract</title>
In this paper, in the first part, we will improve and extend the main results 1 and 2 of Mishra et al. [6] in a <italic>b</italic>-metric space, and in the second and last part, we will improve and extend Theorem 5 and Theorem 6 of Shah [7] in a <italic>b</italic>-metric-like space, in both sections, we will use our new notion of occasionally weakly biased maps of type (𝒜). Some illustrative examples are given in order to clarify and support our findings.
</abstract>

Unique common fixed point results for two maps in incomplete spaces

<abstract>
<title style='display:none'>Abstract</title>
This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments.
This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions.
</abstract>

Variational and numerical analysis of a dynamic elasto-viscoplastic piezoelectric frictional contact problem

<abstract>
<title style='display:none'>Abstract</title>
We investigate random variables for which the variance and the information potential satisfy a preservation law.
</abstract>

Variance and information potential of some random variables

<abstract><title style='display:none'>Abstract</title>In this scientific note, an operator, which is the well-known Tremblay operator in the literature, is first introduced and some of its applications to certain analytic complex functions, which are normalized and analytic in the open unit disk, are then determined. In addition, certain special results of the related applications are also emphasized.</abstract>

Certain basic information related to the Tremblay operator and some applications in connection therewith

<abstract><title style='display:none'>Abstract</title>In this study, the author has established a new lemma and Bullen-type inequalities for conformable fractional integrals. Also, it is given some applications involving Bullen type integral inequalities for differentiable functions to show the results.</abstract>

Some Bullen-type inequalities for conformable fractional integrals

<abstract><title style='display:none'>Abstract</title>Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.</abstract>

Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

<abstract><title style='display:none'>Abstract</title>By this research notes, the well-known Tremblay operator and certain core knowledge therewith are firstly introduced and an extensive result containing numerous (analytic and) geometric properties (of possible applications of the related operator) along with a number of special implications are then constituted. As method for proving, the well-known assertion proposed by [8] is also considered there.</abstract>

Geometric properties of some applications of the Tremblay operator

<abstract>
<title style='display:none'>Abstract</title>
In this investigation, we introduce a new <italic>q</italic>-differential operator that generalizes the well-known Opoola differential operator. Using the operator, we define a family of <italic>q</italic>-bounded turning functions. The new class is denoted by ℛ<italic>qn</italic> (<italic>µ, β, τ </italic>; <italic>λ</italic>). Afterwards, inclusion, characterisation, growth, distortion, covering, linear combination and neighborhood properties of functions <italic>f ∈ </italic>ℛ<italic>qn</italic> (<italic>µ, β, τ </italic>; <italic>λ</italic>) are presented.
</abstract>

Some Properties of a Family of Univalent Functions Defined by a Generalized Opoola Differential Operator

<abstract><title style='display:none'>Abstract</title>In the present investigation, by making use of strong differential subordinations and superordinations, we introduce and study two new classes of holomorphic functions containing generalized differential operator. Also we determine important properties for functions belongs to these classes.</abstract>

Two New Classes of Analytic Functions Defined by Strong Differential Subordinations and Superordinations

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General Mathematics

 Publishing House and Owner: Lucian Blaga University of Sibiu, Romania   General Mathematics publishes high quality papers on pure and applied...

 Publishing House and Owner: Lucian Blaga University of Sibiu, Romania   General Mathematics publishes...

General Mathematics

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