<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper we consider a class of integral equations associated with the invariant mean value property of hyperbolic harmonic functions. We have shown that nonconstant solutions of these integral equations are functions of unbounded variations and do not attain their supremum or infimum on [0; 1): We present an algorithm to obtain numerical solutions of these integral equations. We also consider the equivalent ordinary differential equations and used MATLAB to obtain numerical solutions of these differential equations. </p></abstract>

In this paper we consider a class of integral equations associated with the invariant mean value property of hyperbolic harmonic functions. We have shown that nonconstant solutions of these integral equations are functions of unbounded variations and do not attain their supremum or infimum on [0; 1): We present an algorithm to obtain numerical solutions of these integral equations. We also consider the equivalent ordinary differential equations and used MATLAB to obtain numerical solutions of these differential equations.

Hyperbolic harmonic functions and the associated integral equations

P.G. Department of Mathematics Utkal University Vanivihar, Bhubaneswar, 751004, Odisha, India

Department of Computer and Information Sciences University of Hyderabad Hyderabad, India-500046

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Hyperbolic harmonic functions and the associated integral equations"}

In this paper we consider a class of integral equations associated with the invariant mean value property of hyperbolic harmonic functions. We have shown that...

Hyperbolic harmonic functions and the associated integral equations

Published Online: Dec 12, 2015

Page range: 37 - 56

Received: Sep 09, 2014

Accepted: Jul 05, 2015

DOI: https://doi.org/10.1515/awutm-2015-0003

Keywords
Bergman space, Berezin transform, hyperbolic harmonic functions, invariant mean-value property, integral equations

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Hyperbolic harmonic functions and the associated integral equations

Published Online: Dec 12, 2015

Page range: 37 - 56

Received: Sep 09, 2014

Accepted: Jul 05, 2015

DOI: https://doi.org/10.1515/awutm-2015-0003

KeywordsBergman space, Berezin transform, hyperbolic harmonic functions, invariant mean-value property, integral equations

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Bergman space, Berezin transform, hyperbolic harmonic functions, invariant mean-value property, integral equations