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

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>

Badji Mokhtar-Annaba University Faculty of Sciences

Department of Mathematics Laboratory of Applied Mathematics

Chadli Ben Djedid University Faculty of Sciences and Technology

Unique common fixed point results for two maps in incomplete spaces

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

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>

Bahauddin Zakariya University Centre for Advanced Studies in Pure and Applied Mathematics

Faculty of Sciences Department of Mathematics

Iterative methods for solving scalar equations

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

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

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"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mrow><mi>D</mi></mrow><mi>q</mi></msub><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mi>z</mi></mfrac><mrow><mo>{</mo> <mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>★</mo><mfrac><mi>z</mi><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>-</mo><mi>q</mi><mi>z</mi></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mn>1</mn><mi>z</mi></mrow><mo>)</mo></mrow></mrow></mfrac></mrow> <mo>}</mo></mrow><mo>,</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi>f</mi><mo>∈</mo><mi>𝒜</mi><mo>,</mo><mi> </mi><mi> </mi><mi> </mi><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></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 xmlns="http://www.w3.org/1999/xhtml">

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>

Kasdi Merbah University Department of Mathematics

University of El-Oued Department of Mathematics

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

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

We investigate random variables for which the variance and the information potential satisfy a preservation law.
</abstract>

Faculty of Automation and Computer Science Department of Mathematics

Lucian Blaga University of Sibiu, Faculty of Science

Department of Mathematics and Informatics

Variance and information potential of some random variables

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General Mathematics

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

Unique common fixed point results for two maps in incomplete spaces

Iterative methods for solving scalar equations

On related fixed points in two d-complete topological spaces

On analytic functions related with q-generalized bounded Mocanu variation

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

Variance and information potential of some random variables

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