<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Unbounded solutions for the iterative-difference equation
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2017-0015_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><msup><mtext>f</mtext><mn>2</mn></msup><mo stretchy="false">(</mo><mtext>x</mtext><mo stretchy="false">)</mo><mo>=</mo><mo>λ</mo><mtext>f</mtext><mo stretchy="false">(</mo><mtext>x</mtext><mo>+</mo><mtext>a</mtext><mo stretchy="false">)</mo><mo>+</mo><mo>μ</mo><mtext>x</mtext><mo>,</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>x</mtext><mo>∈</mo><mo>ℝ</mo><mo>,</mo></math><tex-math>\font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} + {\rm{a}}) + \mu {\rm{x}},\;\;\;{\rm{x}} \in {\msbm R},$$</tex-math></alternatives></disp-formula>
have been considered in [Continuous solutions of an iterative-difference equation and Brillouët problem, Publ. Math. Debrecen, 78 (2011), 613–624], where λ, μ, a are real constants. In this paper, we continue to study the solutions not being included there, and further give the convex and concave ones. Finally, continuous solutions of this equation with an extra item were also given, which continuously depend on the parameter a.</p></abstract>

Unbounded solutions for the iterative-difference equation
f2(x)=λf(x+a)+μx,   x∈ℝ,\font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} + {\rm{a}}) + \mu {\rm{x}},\;\;\;{\rm{x}} \in {\msbm R},$$
have been considered in [Continuous solutions of an iterative-difference equation and Brillouët problem, Publ. Math. Debrecen, 78 (2011), 613–624], where λ, μ, a are real constants. In this paper, we continue to study the solutions not being included there, and further give the convex and concave ones. Finally, continuous solutions of this equation with an extra item were also given, which continuously depend on the parameter a.

Unbounded solutions of an iterative-difference equation

Physics and Information Engineering Jiaxing University

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Unbounded solutions of an iterative-difference equation"}

Unbounded solutions for the iterative-difference equation
f2(x)=λf(x+a)+μx,   x∈ℝ,\font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} +...

Unbounded solutions of an iterative-difference equation

Published Online: Aug 05, 2017

Page range: 224 - 234

Received: Apr 26, 2017

DOI: https://doi.org/10.1515/ausm-2017-0015

Keywords
iterative-difference equation, existence, unbounded solution, convex solution, concave solution

© 2017 Lin Li et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Unbounded solutions of an iterative-difference equation

Published Online: Aug 05, 2017

Page range: 224 - 234

Received: Apr 26, 2017

DOI: https://doi.org/10.1515/ausm-2017-0015

Keywordsiterative-difference equation, existence, unbounded solution, convex solution, concave solution

© 2017 Lin Li et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
iterative-difference equation, existence, unbounded solution, convex solution, concave solution