Matematik Bölümünde 09.05.2016 tarihli seminer

09.05.2016

09.05.2016 Pazartesi günü C Blok toplantı salonunda Dr. Hüseyin Işık tarafından "Some Fixed Point Theorems with Applications" başlıklı Matematik semineri verildi.

Bu sunumda Dr. Işık, sabit noktanın varlığının matematik ve pek çok fen bilimi için çok önemli bir değere sahip olmasından, bu konuda elde ettiği sonuçlardan ve uygulamalarından bahsetti.

Some Fixed Point Theorems with Applications
HÜSEYIN ISIK*
* Department of Mathematics, Faculty of Science, Gazi University, 06500-Teknikokullar, Ankara, Turkey,
isikhuseyin76@gmail.com
Abstract
In a wide range of mathematical problems, the existence of a solution is equivalent to the
existence of a fixed point for a suitable map. The existence of a fixed point is therefore of
paramount importance in several areas of mathematics and other sciences. Fixed point results
provide conditions under which maps have solutions. In particular, fixed point techniques
have been applied in such diverse fields as biology, chemistry, computer science, economics,
engineering, game theory and physics (for example, see [1–4]).
In this study, we investigate fixed point results obtained in [5], after giving a brief introduction
of fixed point theory.
References
[1] R.P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge
University Press, New York, (2001).
[2] K.C. Border, Fixed Point Theorems with Applications to Economics and Game Theory,
Cambridge University Press, New York, (1985).
[3] A. Cataldo, E.A. Lee, X. Liu, E.D. Matsikoudis, H. Zheng, A constructive Fixed point
theorem and the feedback semantics of timed systems, Technical Report UCB/EECS-
2006-4, EECS Dept., University of California, Berkeley (2006).
[4] A. Hyvärinen, Fast and robust fixed-point algorithms for independent component analysis,
IEEE Trans. Neural Netw. 10 (3) (1999) 626-634.
[5] H. Isık, D. Türkoglu, Generalized weakly -contractive mappings and applications to
ordinary differential equations, Miskolc Mathematical Notes (in press).