<abstract xmlns="http://www.w3.org/1999/xhtml"> We present some results and open problems in the Calculus of Variations.</abstract>

Some Problems in the Calculus of Variations

<abstract xmlns="http://www.w3.org/1999/xhtml"> Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.</abstract>

On Orthogonally Additive Functions With Big Graphs

<abstract xmlns="http://www.w3.org/1999/xhtml"> On a commutative ring R we study outer measures induced by measures on Spec(R). The focus is on examples of such outer measures and on subsets of R that satisfy the Carathéodory condition.</abstract>

Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

<abstract xmlns="http://www.w3.org/1999/xhtml"> Let E be a complete uniform topological algebra with Arens-Michael normed factors <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/amsil-2017-0002_001.jpg"></inline-graphic> within an algebra isomorphism ϕ. If each factor Eα is complete, then every multiplier of E is continuous and ϕ is a topological algebra isomorphism where M(E) is endowed with its seminorm topology. </abstract>

Multipliers of Uniform Topological Algebras

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables. </abstract>

Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements

<abstract xmlns="http://www.w3.org/1999/xhtml"> Based on a characterization of logarithmic functions due to Heuvers we develop analogous results for multiplicative, exponential and additive functions, respectively.</abstract>

Complementary Results to Heuvers’s Characterization of Logarithmic Functions

<abstract xmlns="http://www.w3.org/1999/xhtml"> Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.</abstract>

A Generalization of m-Convexity and a Sandwich Theorem

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.</abstract>

Invariant Means on Banach Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.</abstract>

Lie Derivations on Trivial Extension Algebras

<abstract xmlns="http://www.w3.org/1999/xhtml"> We give some stability results for the functional equation a(xy) = a(x) + a(y), where a: G → E, G being a groupoid and E a Banach space.</abstract>

On Stability of the Cauchy Functional Equation in Groupoids

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.</abstract>

A Simple Proof of the Polar Decomposition Theorem

<abstract xmlns="http://www.w3.org/1999/xhtml"> In our previous work titled “Fixed Point Results Satisfying Rational type Contractive Conditions in Complex Valued Metric Spaces”[Ann. Math. Sil. 30 (2016), 89-110], some errors has been made in the main results (Theorem 3.1, Theorem 3.7 and Theorem 3.22), that may misguide the readers. This note provides corrections of these errors.</abstract>

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

Report of Meeting. The Seventeenth Katowice–Debrecen Winter Seminar Zakopane (Poland), February 1–4, 2017

AHEAD OF PRINT

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

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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 