headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
Vol. 68, Issue 3
Vol. 68, Issue 2
Vol. 68, Issue 1
» 2018
» 2017
» 2016
» 2015
» 2014
» 2013
» 2012
» 2011
» 2010
» 2009
» 2008
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

Novel results on a fixed function and their application based on the best approximation of the treatment plan for tumour patients getting intensity modulated radiation therapy (IMRT); pp. 223–234

(Full article in PDF format) https://doi.org/10.3176/proc.2019.3.01


Authors

Pooja Dhawan, Jatinderdeep Kaur, Vishal Gupta

Abstract

In the present paper, we extend the concept of contraction in a new manner by introducing D-contraction defined on a family F of bounded functions. We also introduce a new notion of a fixed function on a metric space. Some fixed function theorems along with illustrative examples and application are also given to verify the effectiveness of our results.

 

Keywords

fixed function, complete metric space, D-contraction, α ѱ contractive mapping.

References

1.  Aggarwal , R. P. , Meehan , M. , and O’Regan , D. Fixed Point Theory and Applications. Cambridge University Press , Cambridge , UK , 2001.
https://doi.org/10.1017/CBO9780511543005

2. Banach , S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. , 1922 , 3 , 133–181.
https://doi.org/10.4064/fm-3-1-133-181

3. Border , K. C. Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press , UK , 1985.
https://doi.org/10.1017/CBO9780511625756

4. Bortfeld , T. Optimized planning using physical objectives and constraints. Semin. Radiat. Oncol. , 1999 , 9 , 20–34.
https://doi.org/10.1016/S1053-4296(99)80052-6

5. Chandok , S. and Narang , T. D. Some common fixed point theorems for Banach operator pairs with applications in best approx-imation. Nonlinear Anal.: Theory , Methods Appl. , 2010 , 73 , 105–109.

6. Gupta , V. , Shatanawi , W. , and Mani , N. Fixed point theorems for (y;b )-Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations. JFPTA , 2017 , 19 , 1251–1267.
https://doi.org/10.1007/s11784-016-0303-2

7. Gupta , V. and Kanwar , A. 2016. V-Fuzzy metric space and related fixed point theorems. Fixed Point Theory Appl. , 2016 , 2016: 51.

8. Kannan , R. Some results on fixed points. Bull. Calcutta Math. Soc. , 1968 , 25 , 71–76.

9. Reich , S. Some remarks concerning contraction mappings. Canadian Math. Bull. , 1971 , 14 , 121–124.
https://doi.org/10.4153/CMB-1971-024-9

10. Rhoades , B. E. A comparison of various definitions of contractive mappings. Trans. Amer. Math. Soc. , 1977 , 25 , 257–290.
https://doi.org/10.1090/S0002-9947-1977-0433430-4

11. Samet , B. , Vetro , C. , and Vetro , P. Fixed point theorems for αѱ contractive type mappings. Nonlinear Anal. , 2012 , 75 , 2154–2165.
https://doi.org/10.1016/j.na.2011.10.014

12. Shahi , P. , Kaur , J. , and Bhatia , S. S. Fixed point theorems for (ξ ,α)-expansive mappings in complete metric space. Fixed Point Theory Appl. , 2012 , 2012: 157.

13. Shepard , D. M. , Olivera , G. H. , Reckwerdt , P. J. , and Mackie , T. R. Iterative approaches to dose optimization in tomotherapy. Phys. Med. Biol. , 2000 , 45 , 69–90.
https://doi.org/10.1088/0031-9155/45/1/306

14. Tian , Z. , Zarepisheh , M. , Jia , X. , and Jiang , S. B. 2013. The fixed-point iteration method for IMRT optimization with truncated dose deposition coefficient matrix. arXiv: 1303.3504 [physics.med-ph].

 
Back

Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December