Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x))
This work deals with Feigenbaum’s functional equation f(φ(x))=φp(f(x)), φ(0)=1, 0≤φ(x)≤1, x∈ [0, 1], where p≥2 is an integer, φp is the p-fold iteration of φ, and f(x) is a strictly increasing continuous function on [0, 1] that satisfies f(0)=0, f(x)<x, (x∈(0, 1]). Using a constructive method, we...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/731863 |
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| _version_ | 1832552379789082624 |
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| author | Min Zhang |
| author_facet | Min Zhang |
| author_sort | Min Zhang |
| collection | DOAJ |
| description | This work deals with Feigenbaum’s functional equation f(φ(x))=φp(f(x)), φ(0)=1, 0≤φ(x)≤1, x∈ [0, 1], where p≥2 is an integer, φp is the p-fold iteration of φ, and f(x) is a strictly increasing continuous function on [0, 1] that satisfies f(0)=0, f(x)<x, (x∈(0, 1]). Using a constructive method, we discuss the existence of non-single-valley continuous solutions of the above equation. |
| format | Article |
| id | doaj-art-a6e70cd32eeb44e0b0083e88ea8d8217 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a6e70cd32eeb44e0b0083e88ea8d82172025-02-03T05:58:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/731863731863Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x))Min Zhang0College of Science, China University of Petroleum, Qingdao, Shandong 266555, ChinaThis work deals with Feigenbaum’s functional equation f(φ(x))=φp(f(x)), φ(0)=1, 0≤φ(x)≤1, x∈ [0, 1], where p≥2 is an integer, φp is the p-fold iteration of φ, and f(x) is a strictly increasing continuous function on [0, 1] that satisfies f(0)=0, f(x)<x, (x∈(0, 1]). Using a constructive method, we discuss the existence of non-single-valley continuous solutions of the above equation.http://dx.doi.org/10.1155/2014/731863 |
| spellingShingle | Min Zhang Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) Abstract and Applied Analysis |
| title | Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) |
| title_full | Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) |
| title_fullStr | Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) |
| title_full_unstemmed | Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) |
| title_short | Non-Single-Valley Solutions for p-Order Feigenbaum’s Type Functional Equation f(φ(x))=φp(f(x)) |
| title_sort | non single valley solutions for p order feigenbaum s type functional equation f φ x φp f x |
| url | http://dx.doi.org/10.1155/2014/731863 |
| work_keys_str_mv | AT minzhang nonsinglevalleysolutionsforporderfeigenbaumstypefunctionalequationfphxphpfx |