Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity
We continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact intervals (in midpoint-radius representation) and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/4/114 |
| _version_ | 1818142963846348800 |
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| author | Luciano Stefanini Laerte Sorini Benedetta Amicizia |
| author_facet | Luciano Stefanini Laerte Sorini Benedetta Amicizia |
| author_sort | Luciano Stefanini |
| collection | DOAJ |
| description | We continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact intervals (in midpoint-radius representation) and basic results on convergence and limits, continuity, gH-differentiability, and monotonicity. We define different types of (local) minimal and maximal points and develop the basic theory for their characterization. We then consider some interesting connections with applied geometry of curves and the convexity of interval-valued functions is introduced and analyzed in detail. Further, the periodicity of interval-valued functions is described and analyzed. Several examples and pictures accompany the presentation. |
| first_indexed | 2024-12-11T11:24:08Z |
| format | Article |
| id | doaj.art-2581ba0f72724517bb20ca902c3c35b8 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-11T11:24:08Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-2581ba0f72724517bb20ca902c3c35b82022-12-22T01:09:04ZengMDPI AGAxioms2075-16802019-10-018411410.3390/axioms8040114axioms8040114Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, PeriodicityLuciano Stefanini0Laerte Sorini1Benedetta Amicizia2Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, ItalyDepartment of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, ItalyDepartment of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, ItalyWe continue the presentation of new results in the calculus for interval-valued functions of a single real variable. We start here with the results presented in part I of this paper, namely, a general setting of partial orders in the space of compact intervals (in midpoint-radius representation) and basic results on convergence and limits, continuity, gH-differentiability, and monotonicity. We define different types of (local) minimal and maximal points and develop the basic theory for their characterization. We then consider some interesting connections with applied geometry of curves and the convexity of interval-valued functions is introduced and analyzed in detail. Further, the periodicity of interval-valued functions is described and analyzed. Several examples and pictures accompany the presentation.https://www.mdpi.com/2075-1680/8/4/114interval-valued gh-differencecomparison indexpartial orderslattice of real intervalsconvex interval functionsperiodic interval functions |
| spellingShingle | Luciano Stefanini Laerte Sorini Benedetta Amicizia Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity Axioms interval-valued gh-difference comparison index partial orders lattice of real intervals convex interval functions periodic interval functions |
| title | Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity |
| title_full | Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity |
| title_fullStr | Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity |
| title_full_unstemmed | Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity |
| title_short | Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable—Part II: Extremal Points, Convexity, Periodicity |
| title_sort | interval analysis and calculus for interval valued functions of a single variable part ii extremal points convexity periodicity |
| topic | interval-valued gh-difference comparison index partial orders lattice of real intervals convex interval functions periodic interval functions |
| url | https://www.mdpi.com/2075-1680/8/4/114 |
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