Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class

Abstract There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing t...

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Autores principales:	Stevo Stević, Bratislav Iričanin, Witold Kosmala, Zdeněk Šmarda
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Difference equation Theoretical solvability Practical solvability Equations solvable in a closed form Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3bd212bb82934d53817120926d571d22
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spelling	oai:doaj.org-article:3bd212bb82934d53817120926d571d222021-11-21T12:28:44ZNote on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class10.1186/s13660-021-02720-w1029-242Xhttps://doaj.org/article/3bd212bb82934d53817120926d571d222021-11-01T00:00:00Zhttps://doi.org/10.1186/s13660-021-02720-whttps://doaj.org/toc/1029-242XAbstract There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing the hyperbolic-cotangent one. Our analysis shows a bit unexpected fact, namely that the solvability of the class is based on some algebraic relations, not closely related to some trigonometric ones, which enable us to solve them in an elegant way. Some examples of the difference equations belonging to the class which are practically solvable are presented, as well as some interesting comments on connections of the equations with some iteration processes.Stevo StevićBratislav IričaninWitold KosmalaZdeněk ŠmardaSpringerOpenarticleDifference equationTheoretical solvabilityPractical solvabilityEquations solvable in a closed formMathematicsQA1-939ENJournal of Inequalities and Applications, Vol 2021, Iss 1, Pp 1-12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Difference equation Theoretical solvability Practical solvability Equations solvable in a closed form Mathematics QA1-939
spellingShingle	Difference equation Theoretical solvability Practical solvability Equations solvable in a closed form Mathematics QA1-939 Stevo Stević Bratislav Iričanin Witold Kosmala Zdeněk Šmarda Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
description	Abstract There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing the hyperbolic-cotangent one. Our analysis shows a bit unexpected fact, namely that the solvability of the class is based on some algebraic relations, not closely related to some trigonometric ones, which enable us to solve them in an elegant way. Some examples of the difference equations belonging to the class which are practically solvable are presented, as well as some interesting comments on connections of the equations with some iteration processes.
format	article
author	Stevo Stević Bratislav Iričanin Witold Kosmala Zdeněk Šmarda
author_facet	Stevo Stević Bratislav Iričanin Witold Kosmala Zdeněk Šmarda
author_sort	Stevo Stević
title	Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
title_short	Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
title_full	Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
title_fullStr	Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
title_full_unstemmed	Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
title_sort	note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/3bd212bb82934d53817120926d571d22
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Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class

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