<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

Publié en ligne: 05 août 2017

Pages: 224 - 234

Reçu: 26 avr. 2017

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

Mots clés
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

Publié en ligne: 05 août 2017

Pages: 224 - 234

Reçu: 26 avr. 2017

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

Mots clésiterative-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.

Mots clés
iterative-difference equation, existence, unbounded solution, convex solution, concave solution