Refinements of Caristis fixed point theorem
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Authors
Hassen Aydi
- Department of Mathematics, College of Education of Jubail, University of Dammam, P. O: 12020, Industrial Jubail 31961, Saudi Arabia.
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
Dong Zhang
- School of Mathematical Sciences, Peking University, 100871, Beijing, China.
Abstract
In this paper, we introduce new types of Caristi fixed point theorem and Caristi-type cyclic maps in
a metric space with a partial order or a directed graph. These types of mappings are more general than
that of Du and Karapinar [W.-S. Du, E. Karapinar, Fixed Point Theory Appl., 2013 (2013), 13 pages]. We
obtain some fixed point results for such Caristi-type maps and prove some convergence theorems and best
proximity results for such Caristi-type cyclic maps. It should be mentioned that in our results, all the optional
conditions for the dominated functions are presented and discussed to our knowledge, and the replacing of
\(d(x; Tx)\) by \(\min\{d(x; Tx); d(Tx; Ty)\}\) endowed with a graph makes our results strictly more general. Many
recent results involving Caristi fixed point or best proximity point can be deduced immediately from our
theory. Serval applications and examples are presented making effective the new concepts and results. Two
analogues for Banach-type contraction are also provided.
Share and Cite
ISRP Style
Hassen Aydi, Dong Zhang, Refinements of Caristis fixed point theorem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4084--4097
AMA Style
Aydi Hassen, Zhang Dong, Refinements of Caristis fixed point theorem. J. Nonlinear Sci. Appl. (2016); 9(6):4084--4097
Chicago/Turabian Style
Aydi, Hassen, Zhang, Dong. "Refinements of Caristis fixed point theorem." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4084--4097
Keywords
- Caristi fixed point theorem
- cyclic map
- Banach fixed point theorem.
MSC
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