Fixed points of some set-valued F-contractions


Authors

Zeqing Liu - Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, P. R. China. Xue Na - Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, P. R. China. Young Chel Kwun - Department of Mathematics, Dong-A University, Busan 49315, Korea. Shin Min Kang - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea. - Center for General Education, China Medical University, Taiwan, Taichung 40402, Taiwan.


Abstract

Fixed point theorems of several set-valued F-contractions without using the Hausdorff metric are provided. Our results extend substantially the results due to Nadler [S. B. Nadler, Jr., Pacific J. Math., 30 (1969), 475-488] and Mizoguchi and Takahashi [N. Mizoguchi, W. Takahashi, J. Math. Anal. Appl., 141 (1989), 177-188]. Five nontrivial examples are given.


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