Open Access Published by De Gruyter Open Access

Volume 47 Issue 2

Issue of Demonstratio Mathematica

Contents
Journal Overview

Open Access June 6, 2014

De Morgan Functions and Free De Morgan Algebras

Yu. M. Movsisyan, V. A. Aslanyan, Alex Manoogian

Page range: 271-283

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Abstract

It is commonly known that the free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free bounded distributive lattice on n free generators is isomorphic to the bounded lattice of monotone Boolean functions of n variables. In this paper, we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. This is a solution of the problem suggested by B. I. Plotkin.

Open Access June 6, 2014

Endomorphisms of Implication Algebras

H. Gaitán

Page range: 284-288

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Abstract

In this note we prove that if two implication algebras have isomorphic monoids of endomorphisms then they are isomorphic.

Open Access June 6, 2014

Semidirect Product of Groupoids and Associated Algebras

Leszek Pysiak, Michał Eckstein, Michał Heller, Wiesław Sasin

Page range: 289-299

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Abstract

One of the pressing problems in mathematical physics is to find a generalized Poincaré symmetry that could be applied to nonflat space-times. As a step in this direction, we define the semidirect product of groupoids Γ 0 ⋊ Γ 1 and investigate its properties. We also define the crossed product of a bundle of algebras with the groupoid Γ 1 and prove that it is isomorphic to the convolutive algebra of the groupoid Γ 0 ⋊ Γ 1 . We show that families of unitary representations of semidirect product groupoids in a bundle of Hilbert spaces are random operators. An important example is the Poincaré groupoid defined as the semidirect product of the subgroupoid of generalized Lorentz transformations and the subgroupoid of generalized translations.

Open Access June 6, 2014

Inequalities and Means from a Cyclic Differential Equation

Gerd Herzog, Peer Chr. Kunstmann

Page range: 300-309

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Abstract

We prove that the solution of the cyclic initial value problem u’ k = 1/2 - u k /(u k+1 + u k+2 ) (k Z/nZ), u(0)= x is convergent to an equilibrium μ (x) (1,…,1), and study the properties of the function x → μ(x) and its relation to Shapiro’s inequality.

Open Access June 6, 2014

Generalized Elliptic-Type Integrals and Generating Functions

V. B. L. Chaurasia, Yudhveer Singh

Page range: 310-323

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Abstract

On account of analytical importance or application in certain problems in radiation physics and nuclear technology, several interesting families of elliptic-type integrals were recently studied by many authors. The aim and objective of present paper is to obtain certain new theorems on generating functions. The results obtained in this paper are of manifold generality and basic in nature. In addition, to deriving known and various new elliptic-type integrals and their generalizations, these theorems can be used to evaluate various Euler-type integrals involving a number of generating functions.

Open Access June 6, 2014

On A System of Rational Difference Equation

Qamar Din

Page range: 324-335

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Abstract

In this paper, we study local asymptotic stability, global character and periodic nature of solutions of the system of rational difference equations given by x n +1= , y n =, n=0, 1,…, where the parameters a; b; c; d; e; f ∊ (0; ∞), and with initial conditions x 0 ; y 0 ∊ (0; ∞). Some numerical examples are given to illustrate our results.

Open Access June 6, 2014

Direct Estimate for Some Operators of Durrmeyer Type in Exponential Weighted Space

Grażyna Krech, Eugeniusz Wachnicki

Page range: 336-349

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Abstract

In the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.

Open Access June 6, 2014

Crossed Product of a C*-Algebra by a Semigroup of Interactions

B. K. Kwaśniewski

Page range: 350-370

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Abstract

The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev’s crossed product by an endomorphism, and is related to Exel’s interactions. One of the main goals is the Isomorphism Theorem established in the case of actions by endomorphisms.

Open Access June 6, 2014

Weak Convergence for Nonself Nearly Asymptotically Nonexpansive Mappings by Iterations

Safeer Hussain Khan

Page range: 371-381

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Abstract

In this paper, we obtain a couple of weak convergence results for nonself nearly asymptotically nonexpansive mappings. Our first result is for the Banach spaces satisfying Opial condition and the second for those whose dual satisfies the Kadec-Klee property.

Open Access June 6, 2014

Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

P. Cholamjiak, W. Cholamjiak, S. Suantai

Page range: 382-395

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Abstract

In this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

Open Access June 6, 2014

Common Fixed Point of Four Mappings Satisfying Implicit Generalized Weak Contractive Type Condition

Shaban Sedghi, Nabi Shobe, Mujahid Abbas

Page range: 396-410

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Abstract

In this paper, common fixed point for four maps using an implicit contractive condition in a complete metric space is proved. Some periodic point results for such mappings are also obtained. These results extend and generalize several comparable results in the current literature.

Open Access June 6, 2014

Extended Weyl-Type Theorems for Direct Sums

M. Berkani, M. Kachad, H. Zariouh

Page range: 411-422

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Abstract

In this paper, we study the stability of extended Weyl and Browdertype theorems for orthogonal direct sum S⊕T, where S and T are bounded linear operators acting on Banach space. Two counterexamples shows that property (ab), in general, is not preserved under direct sum. Nonetheless, and under the assumptions that Π 0 α (T) ⊂σ α (S) and Π 0 α (S) ⊂σ α (T), we characterize preservation of property (ab) under direct sum S⊕T. Furthermore, we show that if S and T satisfy generalized a-Browder’s theorem, then S⊕T satisfies generalized a-Browder’s theorem if and only if σ SBF - + (S ⊕T) = σ SBF - + (S) ∪ σSBF - + (T), which improves a recent result of [13] by removing certain extra assumptions.

Open Access June 6, 2014

Some Applications of Minimal P_γ -Open Sets

Alias B. Khalaf, Hariwan Z. Ibrahim

Page range: 423-432

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Abstract

We characterize minimal P γ-open sets in topological spaces. We show that any nonempty subset of a minimal P γ-open set is pre P-open. As an application of a theory of minimal Pγ-open sets, we obtain a sufficient condition for a P-locally finite space to be a pre P γ-Hausdorff space

Open Access June 6, 2014

R_δ-Supercontinuous Functions

J. K. Kohli, B. K. Tyagi, D. Singh, Jeetendra Aggarwal

Page range: 433-448

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Abstract

A new class of functions called ‘R δ -supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of R z -supercontinuous functions which in its turn properly contains the class of R cl - supercontinuous functions (Demonstratio Math. 46(1) (2013), 229-244) and so includes all R cl -supercontinuous (≡clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293-300; Indian J. Pure Appl. Math. 14(6) (1983), 767-772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703-723).

Open Access June 6, 2014

Two Generalized Common Fixed Point Theorems Involving Compatibility and Property E.A.

T. Phaneendra, V. S. R. Prasad

Page range: 449-458

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Abstract

We prove two generalizations: the first to Das and Naik’s theorem for a pair of compatible maps without continuity; and the next as an extension of our first result to three self-maps on a metric space X without compatibility, under a stronger contraction type inequality and restricting the completeness of X to its subspace. The latter is a significant generalization of a recent result of Pant et al.

Open Access June 6, 2014

On the Canonical Connection for Smooth Envelopes

Giovanni Moreno

Page range: 459-464

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Abstract

A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds, which were proposed in the last decades. Such an operation is indispensable in order to perform differential calculus. A derivation of the enveloping algebra can be restricted to the original one, but it is a delicate question if the the viceversa can be done as well. In a physical language, this would correspond to the existence of a canonical connection. In this paper, we show an example of an algebra which always possesses such a connection.

Open Access June 6, 2014

Remarks on Smooth Real-Compactness for Sikorski Spaces

Michał J. Cukrowski, Michał M. Stronkowski

Page range: 465-473

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Abstract

It is known that every Sikorski space with the countably generated differential structure is smoothly real-compact. It means that every homomorphism from its differential structure, which forms a ring of smooth real-valued functions into the ring of real numbers, is an evaluation. This result is sharp: there is a non-smoothly real-compact Sikorski space with the differential structure which is not countably generated. We provide an easy example demonstrating this. By modifying this example we are able to show a certain shortcoming of the generator embedding, comparing to the canonical embedding, for Sikorski spaces. Finally, we note that a homomorphism from the ring of smooth functions of a Sikorski space into the ring of real numbers is an evaluation if and only if it is continuous.

Open Access June 6, 2014

Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform

Krzysztof Bartoszek, Michał Krzeminski

Page range: 474-481

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Abstract

Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this, we correct the proof of Liggett and Schinazi (2009) in the critical case.

Open Access June 6, 2014

An Iterative Method for Symmetric Positive Semidefinite Linear System of Equations

Davod Khojasteh Salkuyeh

Page range: 482-492

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Abstract

In this paper, a new two-step iterative method for solving symmetric positive semidefinite linear system of equations is presented. A sufficient condition for the semiconvergence of the method is also given. Some numerical experiments are presented to show the efficiency of the proposed method.

Open Access June 6, 2014

On Some Consequences of the Functional Generalization of the Parallelogram Identity

Maciej J. Maczyński

Page range: 493-506

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Abstract

The aim of this paper is to unify the partial results, which up to now, have been dispersed in various publications in order to show the importance of the functional form of parallelogram identity in mathematics and physics. We study vector spaces admitting a real non-negative functional which satisfies an identity analogous to the parallelogram identity in normed vector spaces. We show that this generalized parallelogram identity also implies an equality analogous to the Cauchy-Schwarz inequality. We study the consequences of this identity in real and complex vector spaces, in generalized Riesz spaces and in abelian groups. We give a physical interpretation to these results. For vector spaces of observables and states, we show that the parallelogram identity implies an inequality analogous to Heisenberg’s uncertainty principle (HUP), and we show that we can obtain the standard structure of quantum mechanics from the parallelogram identity, without assuming from the beginning the HUP. The role of complex numbers in quantum mechanics is discussed.

Open Access June 6, 2014

Acknowledgement of Priority “Weighted Averages of Random Variables and Exact Weights”

Przemysław Matuła, Michał Seweryn

Page range: 507-508

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About this journal

Demonstratio Mathematica is a fully peer-reviewed, open access, electronic journal devoted to functional analysis, approximation theory and related topics. The journal presents a forum where all aspects of these problems can be discussed. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-term preservation, no space constraints and quick online publication.

Demonstratio Mathematica is listed inter alia by Web of Science (ESCI), SCOPUS, MathSciNet and zbMATH. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.

The potential topics include (but are not limited to):

Approximation theory and iteration methods
Fixed point theory and methods of computing fixed points
Functional, ordinary and partial differential equations
Nonsmooth analysis, variational analysis and convex analysis
Optimization theory, variational inequalities and complementarity problems

For more detailed list of the potential topics please refer to Instruction for Authors.

The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.

Demonstratio Mathematica is subject to an Article Processing Charge (APC). There are no submission charges – Article Processing Charges apply after the acceptance of a manuscript. Authors, who have limited access to funds, may request for a discount. Inquiries concerning APCs should be addressed before or immediately after submission of a paper to the Editorial Office (demonstratio.editorial@degruyter.com). For more details please refer to Article Processing Charges document (in PDF).

Special / Topical Issues:

Development of Fuzzy Sets and Their Extensions
GUEST EDITORS: Željko Stević (University of East Sarajevo, Bosnia and Herzegovina), Yiming Tang (Hefei University of Technology, China), Lei Liu (Liaoning University of Technology, China), Muhammad Gulzar (University of Education Lahore, Pakistan)
DEADLINE FOR SUBMISSIONS: October 16, 2023
2nd International E-Conference on Mathematical and Statistical Sciences: A Selcuk Meeting
GUEST EDITOR: Tuncer Acar (Selçuk University, Turkey)
DEADLINE FOR SUBMISSIONS: August 31, 2023
Dynamic Modeling and Control methods for the Nonlinear system using Artificial Mathematical Intelligence
GUEST EDITORS: B. Nagaraj (Rathinam Group of Institutions, Coimbatore, India), Danilo Pelusi (Communication Engineering, University of Teramo, Italy), Raffaele Mascella (Communication Engineering University of Teramo, Italy)
DEADLINE FOR SUBMISSIONS: July 15, 2023
Recent Developments in Fixed-Point Theory and Applications
GUEST EDITORS: Santosh Kumar (University of Dar es Salaam, Tanzania), Anita Tomar (Sri Dev Suman Uttarakhand University, India), Cristian Chifu (Babes-Bolyai University, Romania), Mohammad Mursaleen (Aligarh Muslim University, India)
DEADLINE FOR SUBMISSIONS: October 10, 2023
On some integral inequalities, integral equations and applications
GUEST EDITORS: Ahmet O. Akdemir (Ağrı İbrahim Çeçen University, Turkey), Maria Alessandra Ragusa (University of Catania, Italy), Nguyen Huy Tuan (Van Lang University, Vietnam)
DEADLINE FOR SUBMISSIONS: October 15, 2023
Nonlinear Evolution Equations and Their Applications
GUEST EDITORS: Praveen Agarwal (Anand International College of Engineering, India), Dumitru Baleanu (Department of Mathematics, Cankaya University, Turkey), Necati Ozdemir (Balikesir University, Turkey), Mohamed S. Osman (Department of Mathematics, Faculty of Science, Cairo University, Egypt)
DEADLINE FOR SUBMISSIONS: August 15, 2023
Mathematics for Artificial intelligence and Artificial intelligence for Mathematics
GUEST EDITORS: Hadi Jahanshahi (University of Manitoba, Canada), Oscar Castillo (Tijuana Institute of Technology, Mexico)
DEADLINE FOR SUBMISSIONS: October 2, 2023
Computational and Numerical Methods for Special Functions
GUEST EDITORS: Serkan Araci (Hasan Kalyoncu University, Turkey), Martin Bohner (Missouri University of Science and Technology, USA), Guotao Wang (Shanxi Normal University, China)
DEADLINE FOR SUBMISSIONS: March 31, 2023.

Volume 47 Issue 2

Issue of Demonstratio Mathematica

De Morgan Functions and Free De Morgan Algebras

Abstract

Endomorphisms of Implication Algebras

Abstract

Semidirect Product of Groupoids and Associated Algebras

Abstract

Inequalities and Means from a Cyclic Differential Equation

Abstract

Generalized Elliptic-Type Integrals and Generating Functions

Abstract

On A System of Rational Difference Equation

Abstract

Direct Estimate for Some Operators of Durrmeyer Type in Exponential Weighted Space

Abstract

Crossed Product of a C*-Algebra by a Semigroup of Interactions

Abstract

Weak Convergence for Nonself Nearly Asymptotically Nonexpansive Mappings by Iterations

Abstract

Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

Abstract

Common Fixed Point of Four Mappings Satisfying Implicit Generalized Weak Contractive Type Condition

Abstract

Extended Weyl-Type Theorems for Direct Sums

Abstract

Some Applications of Minimal Pγ -Open Sets

Abstract

Rδ-Supercontinuous Functions

Abstract

Two Generalized Common Fixed Point Theorems Involving Compatibility and Property E.A.

Abstract

On the Canonical Connection for Smooth Envelopes

Abstract

Remarks on Smooth Real-Compactness for Sikorski Spaces

Abstract

Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform

Abstract

An Iterative Method for Symmetric Positive Semidefinite Linear System of Equations

Abstract

On Some Consequences of the Functional Generalization of the Parallelogram Identity

Abstract

Acknowledgement of Priority “Weighted Averages of Random Variables and Exact Weights”

Some Applications of Minimal P_γ -Open Sets

R_δ-Supercontinuous Functions