Abstract
Two concepts of nonlinear contractions for multi-valued mappings in complete metric spaces are introduced and three fixed point theorems are proved. Presented theorems are generalizations of very recent fixed point theorems due to Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132–139] and Feng and Liu [Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103–112], as well as a fixed point theorem of Mizoguchi and Takahashi [N. Mizoguchi, W. Takahash, Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177–188] and several others. An example is given to show that presented results are genuine generalizations. Our results are also some contribution to an open problem raised by Reich [S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972), 26-42; S. Reich, Some fixed point problems, Atti Acad. Naz. Lincei 57 (1974), 194-198; S. Reich, Some problems and results in fixed point theory, Contemp. Math. 21 (1983), 179–187].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Nonlinear Analysis: Theory, Methods & Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
