Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces
Study of the fixed point for derivative functions is an effort to expand the knowledge of fixed point for functions. This study represents original research on the existence of the fixed point for derivative functions which has been not studied before. Therefore this study attempts to explore the...
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| Format: | Thesis |
| Language: | English |
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2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/83674/ http://psasir.upm.edu.my/id/eprint/83674/1/FS%202019%2022%20-%20IR.pdf |
| _version_ | 1848859604571652096 |
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| author | Muslikh, Mohamad |
| author_facet | Muslikh, Mohamad |
| author_sort | Muslikh, Mohamad |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Study of the fixed point for derivative functions is an effort to expand the knowledge
of fixed point for functions. This study represents original research on the existence of
the fixed point for derivative functions which has been not studied before. Therefore
this study attempts to explore the existence of fixed point for derivative functions.
The research found that the derivative function defined on a closed unit interval into
itself has a fixed point. In addition, this study attempts to extend those results for
the derivative function defined on the whole real number line. By the concepts of
commutativity and compatibility between the function and its derivatives show that
the derivative function of the real-valued function has a fixed point. Meanwhile, in
the case of set-valued function, we use the definition of the generalizations of the
Hukuhara derivative. By using hybrid composite mapping compatible with Hausdorff
metric, this study shows that derivative of the interval-valued function has a fixed
point. Furthermore, based on the absolute derivative notion on metric spaces in the
study of differentiation for single-valued functions, we introduce the new notions
of the "Straddle Lemma" and the class of the "Darboux function". Other results
in this study are the absolute derivative and the metric derivative of the set-valued
functions. This expansion adds the literature on differentiability references for setvalued
functions, among others the continuity of the set-valued function, absolute
derivative of the constant set-valued function, and comparisons with the Hukuhara
derivative and generalization of the Hukuhara derivative. The metric derivative
concept introduced for the set-valued function generates the generalization of the
famous Rademacher’s theorems. |
| first_indexed | 2025-11-15T12:31:59Z |
| format | Thesis |
| id | upm-83674 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:31:59Z |
| publishDate | 2019 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-836742020-10-08T01:30:45Z http://psasir.upm.edu.my/id/eprint/83674/ Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces Muslikh, Mohamad Study of the fixed point for derivative functions is an effort to expand the knowledge of fixed point for functions. This study represents original research on the existence of the fixed point for derivative functions which has been not studied before. Therefore this study attempts to explore the existence of fixed point for derivative functions. The research found that the derivative function defined on a closed unit interval into itself has a fixed point. In addition, this study attempts to extend those results for the derivative function defined on the whole real number line. By the concepts of commutativity and compatibility between the function and its derivatives show that the derivative function of the real-valued function has a fixed point. Meanwhile, in the case of set-valued function, we use the definition of the generalizations of the Hukuhara derivative. By using hybrid composite mapping compatible with Hausdorff metric, this study shows that derivative of the interval-valued function has a fixed point. Furthermore, based on the absolute derivative notion on metric spaces in the study of differentiation for single-valued functions, we introduce the new notions of the "Straddle Lemma" and the class of the "Darboux function". Other results in this study are the absolute derivative and the metric derivative of the set-valued functions. This expansion adds the literature on differentiability references for setvalued functions, among others the continuity of the set-valued function, absolute derivative of the constant set-valued function, and comparisons with the Hukuhara derivative and generalization of the Hukuhara derivative. The metric derivative concept introduced for the set-valued function generates the generalization of the famous Rademacher’s theorems. 2019-03 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/83674/1/FS%202019%2022%20-%20IR.pdf Muslikh, Mohamad (2019) Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces. Doctoral thesis, Universiti Putra Malaysia. Metric spaces Analytic functions |
| spellingShingle | Metric spaces Analytic functions Muslikh, Mohamad Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| title | Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| title_full | Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| title_fullStr | Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| title_full_unstemmed | Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| title_short | Fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| title_sort | fixed point for derivative and differentiation of single-valued and set-valued functions on metric spaces |
| topic | Metric spaces Analytic functions |
| url | http://psasir.upm.edu.my/id/eprint/83674/ http://psasir.upm.edu.my/id/eprint/83674/1/FS%202019%2022%20-%20IR.pdf |