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

Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions.
</abstract>

Refinements of Some Classical Inequalities Involving Sinc and Hyperbolic Sinc Functions

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

Recently, Bród introduced a new Jacobsthal-type sequence which is called <italic>r</italic>-Jacobsthal sequence in current study. After defining the appropriate <italic>r</italic>-Jacobsthal–Lucas sequence for the <italic>r</italic>-Jacobsthal sequence, we obtain some properties of these two sequences. For simpler results, we define two new sequences and examine their properties, too. Finally, we generalize some well-known identities.
</abstract>

Department of Discrete Mathematics, Faculty of Mathematics and Applied Physics

On <italic>r</italic>-Jacobsthal and <italic>r</italic>-Jacobsthal-Lucas Numbers

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

In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example.
</abstract>

Existence, Data Dependence and Stability of Fixed Points of Multivalued Maps in Incomplete Metric Spaces

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

We consider two variants of the sine subtraction law on a semi-group <italic>S</italic>. The main objective is to solve <italic>f</italic>(<italic>xy</italic><italic>∗</italic> ) = <italic>f</italic>(<italic>x</italic>)<italic>g</italic>(<italic>y</italic>) <italic>− g</italic>(<italic>x</italic>)<italic>f</italic>(<italic>y</italic>) for unknown functions <italic>f, g</italic> : <italic>S →</italic> ℂ, where <italic>x</italic> ↦ <italic>x</italic><italic>*</italic> is an anti-homomorphic involution. Until now this equation was not solved even when <italic>S</italic> is a non-Abelian group and <italic>x*</italic> = <italic>x</italic>−1. We find the solutions assuming that <italic>f</italic> is central. A secondary objective is to solve <italic>f</italic>(<italic>xσ</italic>(<italic>y</italic>)) = <italic>f</italic>(<italic>x</italic>)<italic>g</italic>(<italic>y</italic>) <italic>− g</italic>(<italic>x</italic>)<italic>f</italic>(<italic>y</italic>), where <italic>σ</italic> : <italic>S → S</italic> is a homomorphic involution. Until now this variant was solved assuming that <italic>S</italic> has an identity element. We also find the continuous solutions of these equations on topological semigroups.
</abstract>

Sine Subtraction Laws on Semigroups

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

We examine the multiplicity of the greatest prime factor in <italic>k</italic>-full numbers and <italic>k</italic>-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.
</abstract>

Some Observations on the Greatest Prime Factor of an Integer

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

In this research we introduce the concept of strong <italic>m</italic>-convexity for set-valued functions defined on <italic>m</italic>-convex subsets of real linear normed spaces, a variety of properties and examples of these functions are shown, an inclusion of Jensen type is also exhibited.
</abstract>

Universidad de los Andes, Núcleo “Rafael Rangel”

Strong <italic>m</italic>-Convexity of Set-Valued Functions

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

We propose in this study, a new logarithmic barrier approach to solve linear semidefinite programming problem. We are interested in computation of the direction by Newton’s method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost.
Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by some numerical simulations showing the e˙ectiveness of the algorithm developed in this work, which are presented in the last section of this paper.
</abstract>

Logarithmic Barrier Method Via Minorant Function for Linear Semidefinite Programming

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

In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented. Also, the recurrence, generating function, Binet’s formula, and matrix form of Leonardo’s Gaussian and octonion numbers are defined. The development of the Gaussian numbers is performed from the insertion of the imaginary component <italic>i</italic> in the one-dimensional recurrence of the sequence. Regarding the octonions, the terms of the Leonardo sequence are presented in eight dimensions. Furthermore, the generalizations and inherent properties of Leonardo’s Gaussians and octonions are presented.
</abstract>

Federal University of Ceará Fortaleza-CE

University of Trás-os-Montes and Alto Douro Vila Real

The Generalization of Gaussians and Leonardo’s Octonions

AHEAD OF PRINT

Volume 38 (2024): Issue 1 (March 2024)

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Volume 37 (2023): Issue 1 (March 2023)

Volume 36 (2022): Issue 2 (September 2022)

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Volume 35 (2021): Issue 2 (September 2021)

Volume 35 (2021): Issue 1 (February 2021)

Volume 34 (2020): Issue 2 (September 2020)

Volume 34 (2020): Issue 1 (July 2020)

Volume 33 (2019): Issue 1 (September 2019)

Volume 32 (2018): Issue 1 (September 2018)

Volume 31 (2017): Issue 1 (September 2017)

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Annales Mathematicae Silesianae

Annales Mathematicae Silesianae publishes significant research and survey papers from all branches of pure and applied mathematics, and reports of meetings. It welcomes contributed papers that develop important, new mathematical ideas and results or solve outstanding problems.  Article processing chargesThe journal does not have article processing charges (APCs) nor article submission charges.  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.  Peer Review process  Annales Mathematicae Silesianae is a single-blind peer reviewed journal.Normally the papers are peer reviewed by two independent referees who are experts in the appropriate branch of mathematics. According to their opinions the manuscripts are either accepted or rejected. In the case their opinions contradict each other we send the paper to the third reviewer.Reviewers are asked to provide detailed, constructive comments that will help both the editors to make a decision on the publication and the author(s) to improve their manuscript. Preparing the review the reviewers may use the following scheme: review_scheme.pdf. Reviewers are also asked to declare that there is no conflict of interests between them and the authors.  Target Group  - researchers in all branches of pure and applied mathematics 

Annales Mathematicae Silesianae

Volume 37 (2023): Issue 1 (March 2023)

Refinements of Some Classical Inequalities Involving Sinc and Hyperbolic Sinc Functions

On r-Jacobsthal and r-Jacobsthal-Lucas Numbers

Existence, Data Dependence and Stability of Fixed Points of Multivalued Maps in Incomplete Metric Spaces

Sine Subtraction Laws on Semigroups

Some Observations on the Greatest Prime Factor of an Integer

Strong m-Convexity of Set-Valued Functions

Logarithmic Barrier Method Via Minorant Function for Linear Semidefinite Programming

The Generalization of Gaussians and Leonardo’s Octonions

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