Research Article
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Year 2021, Volume: 50 Issue: 1, 79 - 91, 04.02.2021
https://doi.org/10.15672/hujms.644665

Abstract

Project Number

11701425

References

  • [1] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston Inc., Boston, MA, 2001.
  • [2] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • [3] Y. Chalco-Cano, A. Rufián-Lizana, H. Román-Flores and M.D. Jiménez-Gamero, Calculus for interval-valued functions using generalized Hukuhara derivative and applications, Fuzzy Sets Syst. 219, 49–67, 2013.
  • [4] C.G. Gal and S.G. Gal, Semigroups of operators on spaces of fuzzy-number-valued functions with applications to fuzzy differential equations, J. Fuzzy Math. 13, 647– 682, 2005.
  • [5] A.E. Hamza and K.M. Oraby, Semigroups of operators and abstract dynamic equations on time scales, Appl. Math. Comput. 270, 334–348, 2013.
  • [6] S. Hilger, Ein Makettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, 1988.
  • [7] V. Lupulescu, Hukuhara differentiability of interval-valued functions and interval differential equations on time scales, Inform. Sciences, 248, 50–67, 2013.
  • [8] S. Markov, Calculus for interval functions of a real variable, Computing, 22, 325–337, 1979.
  • [9] S. Markov, On the algebraic properties of convex bodies and some applications, J. Convex Anal. 7, 129–166, 2000.
  • [10] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst. 161, 1564–1584, 2010.
  • [11] L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal. 71, 1311–1328, 2009.
  • [12] J. Tao and Z. Zhang, Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations, Adv. Differ. Equ. 2016, Article number: 45, 2016.

Mean value theorem and semigroups of operators for interval-valued functions on time scales

Year 2021, Volume: 50 Issue: 1, 79 - 91, 04.02.2021
https://doi.org/10.15672/hujms.644665

Abstract

In this paper, a new version of mean value theorem for interval-valued functions on time scales is established. Meantime, some basic concepts and results associated with semigroups of operators for interval-valued functions on time scales are presented. As an application of semigroups of operators, under certain conditions, we consider the initial value problem for interval-valued differential equations on time scales. Finally, two issues worthy of further discussion are presented.

Supporting Institution

National Natural Science Foundation of China

Project Number

11701425

References

  • [1] M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser Boston Inc., Boston, MA, 2001.
  • [2] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • [3] Y. Chalco-Cano, A. Rufián-Lizana, H. Román-Flores and M.D. Jiménez-Gamero, Calculus for interval-valued functions using generalized Hukuhara derivative and applications, Fuzzy Sets Syst. 219, 49–67, 2013.
  • [4] C.G. Gal and S.G. Gal, Semigroups of operators on spaces of fuzzy-number-valued functions with applications to fuzzy differential equations, J. Fuzzy Math. 13, 647– 682, 2005.
  • [5] A.E. Hamza and K.M. Oraby, Semigroups of operators and abstract dynamic equations on time scales, Appl. Math. Comput. 270, 334–348, 2013.
  • [6] S. Hilger, Ein Makettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, 1988.
  • [7] V. Lupulescu, Hukuhara differentiability of interval-valued functions and interval differential equations on time scales, Inform. Sciences, 248, 50–67, 2013.
  • [8] S. Markov, Calculus for interval functions of a real variable, Computing, 22, 325–337, 1979.
  • [9] S. Markov, On the algebraic properties of convex bodies and some applications, J. Convex Anal. 7, 129–166, 2000.
  • [10] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst. 161, 1564–1584, 2010.
  • [11] L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal. 71, 1311–1328, 2009.
  • [12] J. Tao and Z. Zhang, Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations, Adv. Differ. Equ. 2016, Article number: 45, 2016.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Yonghong Shen 0000-0002-1525-851X

Project Number 11701425
Publication Date February 4, 2021
Published in Issue Year 2021 Volume: 50 Issue: 1

Cite

APA Shen, Y. (2021). Mean value theorem and semigroups of operators for interval-valued functions on time scales. Hacettepe Journal of Mathematics and Statistics, 50(1), 79-91. https://doi.org/10.15672/hujms.644665
AMA Shen Y. Mean value theorem and semigroups of operators for interval-valued functions on time scales. Hacettepe Journal of Mathematics and Statistics. February 2021;50(1):79-91. doi:10.15672/hujms.644665
Chicago Shen, Yonghong. “Mean Value Theorem and Semigroups of Operators for Interval-Valued Functions on Time Scales”. Hacettepe Journal of Mathematics and Statistics 50, no. 1 (February 2021): 79-91. https://doi.org/10.15672/hujms.644665.
EndNote Shen Y (February 1, 2021) Mean value theorem and semigroups of operators for interval-valued functions on time scales. Hacettepe Journal of Mathematics and Statistics 50 1 79–91.
IEEE Y. Shen, “Mean value theorem and semigroups of operators for interval-valued functions on time scales”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 1, pp. 79–91, 2021, doi: 10.15672/hujms.644665.
ISNAD Shen, Yonghong. “Mean Value Theorem and Semigroups of Operators for Interval-Valued Functions on Time Scales”. Hacettepe Journal of Mathematics and Statistics 50/1 (February 2021), 79-91. https://doi.org/10.15672/hujms.644665.
JAMA Shen Y. Mean value theorem and semigroups of operators for interval-valued functions on time scales. Hacettepe Journal of Mathematics and Statistics. 2021;50:79–91.
MLA Shen, Yonghong. “Mean Value Theorem and Semigroups of Operators for Interval-Valued Functions on Time Scales”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 1, 2021, pp. 79-91, doi:10.15672/hujms.644665.
Vancouver Shen Y. Mean value theorem and semigroups of operators for interval-valued functions on time scales. Hacettepe Journal of Mathematics and Statistics. 2021;50(1):79-91.