<abstract xmlns="http://www.w3.org/1999/xhtml">We study a functional equation first proposed by T. Popoviciu <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_015_w2aab2b8c22b1b7b1ab1ac15Aa">[15]</xref> in 1955. It was solved for the easiest case by Ionescu <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_009_w2aab2b8c22b1b7b1ab1ab9Aa">[9]</xref> in 1956 and, for the general case, by Ghiorcoiasiu and Roscau <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_007_w2aab2b8c22b1b7b1ab1ab7Aa">[7]</xref> and Radó <xref ref-type="bibr" rid="j_amsil-2016-0006_ref_017_w2aab2b8c22b1b7b1ab1ac17Aa">[17]</xref> in 1962. Our solution is based on a generalization of Radó’s theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.</abstract>

On Popoviciu-Ionescu Functional Equation

<abstract xmlns="http://www.w3.org/1999/xhtml">Let ℓ > 2 be a prime number. Let <italic>K</italic> be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group <italic>CK</italic>. The main theorem of the paper gives a sufficient condition for a finite set of primes of <italic>K</italic> to be the wild set of some Hilbert self-equivalence of <italic>K</italic> of degree ℓ.</abstract>

Wild Primes of a Higher Degree Self-Equivalence of a Number Field

<abstract xmlns="http://www.w3.org/1999/xhtml">Some reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.</abstract>

Mathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001,

School of Computer Science & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050,

Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In paper <xref ref-type="bibr" rid="j_amsil-2016-0004_ref_004_w2aab2b8b6b1b7b1ab1ab4Aa">[4]</xref> there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant <italic>λ</italic>. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when <italic>λ</italic> is not constant but a Lipschitz function.</abstract>

Random Dynamical Systems with Jumps and with a Function Type Intensity

<abstract xmlns="http://www.w3.org/1999/xhtml">The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.</abstract>

Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140,

Department of Mathematics, University of Malakand, Chakdara Dir(L),

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In the paper two types of stability and of b-stability of functional equations are distinguished.</abstract>

On the Normal Stability of Functional Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in <xref ref-type="bibr" rid="j_amsil-2016-0002_ref_006_w2aab2b8c18b1b7b1ab1ab6Aa">[6]</xref>, that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in <xref ref-type="bibr" rid="j_amsil-2016-0002_ref_002_w2aab2b8c18b1b7b1ab1ab2Aa">[2]</xref>.</abstract>

Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">We describe some algorithms, without using resolution of singularities, that establish the rationality of the motivic Igusa zeta series of certain hypersurfaces that are non-degenerated with respect to their Newton polyhedron. This includes, in any characteristic, the motivic rationality for polydiagonal hypersurfaces, vertex singularities, binomial hypersurfaces, and Du Val singularities.</abstract>

The Motivic Igusa Zeta Series of Some Hypersurfaces Non-Degenerated with Respect to their Newton Polyhedron

<abstract xmlns="http://www.w3.org/1999/xhtml">Let (<italic>S</italic>, +) be a commutative semigroup, σ : <italic>S</italic> → <italic>S</italic> be an endomorphism with σ2 = <italic>id</italic> and let <italic>K</italic> be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions <italic>f</italic>, <italic>g</italic> : <italic>S</italic> → <italic>K</italic> of the functional equation
<disp-formula id="j_amsil-2016-0007_eq_001_w2aab2b8ab1b7b1aab1c14b1c21Aa"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amsil-2016-0007_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo stretchy="false">)</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi>σ</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mi>g</mi><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>+</mo><mi>g</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi>g</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mtext>for</mtext><mi> </mi><mi> </mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>S</mi><mo>.</mo></math><tex-math>$$f(x + y) + f(x + \sigma (y)) + g(x + y) = 2f(x) + g(x)g(y)\;\;\;\;{\rm for}\;\;x,y \in S.$$</tex-math></alternatives></disp-formula>
We also consider an analogous problem for the Jensen and the d’Alembert equations as well as for the d’Alembert and the exponential Cauchy equations.</abstract>

Alienation of the Jensen, Cauchy and d’Alembert Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of dual spaces.</abstract>

Characterizations of Rotundity and Smoothness by Approximate Orthogonalities

<abstract xmlns="http://www.w3.org/1999/xhtml">We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.</abstract>

The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

<abstract xmlns="http://www.w3.org/1999/xhtml">Almost complete description of abelian groups (<italic>A</italic>, +, 0) such that every associative ring <italic>R</italic> with the additive group <italic>A</italic> satisfies the condition: every subgroup of <italic>A</italic> is an ideal of <italic>R</italic>, is given. Some new results for <italic>SR</italic>-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not <italic>nil</italic>-groups is complemented using only elementary methods.</abstract>

A Note on Additive Groups of Some Specific Associative Rings

Report of Meeting

AHEAD OF PRINT

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

Volume 37 (2023): Issue 2 (September 2023)

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

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

Volume 36 (2022): Issue 1 (March 2022)

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)

Volume 30 (2016): Issue 1 (September 2016)

Volume 29 (2015): Issue 1 (September 2015)

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 