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Fixed Point Theorems for Set-valued Contractions in Complete Metric Spaces by D. Klim; D. Wardowski is a Mathematics article available to read on EtoBox.
What is Fixed Point Theorems for Set-valued Contractions in Complete Metric Spaces about?
The fixed point theory of set-valued contractions which was initiated by Nadler [S.B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969) 475-488] was developed in different directions by many authors, in particular, by [S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972) 26-42; N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; 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]. In the present paper, the concept of contraction for set-valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established. One of our results essentially generalizes the Nadler and Feng-Liu theorems and is different from the Mizoguchi-Takahashi result. The second result is different from the Reich and Mizoguchi-Takahashi results. The method used in the proofs of our results is inspired by Mizoguchi-Takahashi and Feng-Liu's ideas. Comparisons and examples are given.
Who reads Fixed Point Theorems for Set-valued Contractions in Complete Metric Spaces?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- D. Klim; D. Wardowski
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)
- Published
- 2007
- Language
- EN
- Field
- Mathematics (Physical Sciences)