# Convexity of balls and fixed-point theorems for mappings with nonexpansive square

Compositio Mathematica (1970)

- Volume: 22, Issue: 3, page 269-274
- ISSN: 0010-437X

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topGoebel, K.. "Convexity of balls and fixed-point theorems for mappings with nonexpansive square." Compositio Mathematica 22.3 (1970): 269-274. <http://eudml.org/doc/89058>.

@article{Goebel1970,

author = {Goebel, K.},

journal = {Compositio Mathematica},

language = {eng},

number = {3},

pages = {269-274},

publisher = {Wolters-Noordhoff Publishing},

title = {Convexity of balls and fixed-point theorems for mappings with nonexpansive square},

url = {http://eudml.org/doc/89058},

volume = {22},

year = {1970},

}

TY - JOUR

AU - Goebel, K.

TI - Convexity of balls and fixed-point theorems for mappings with nonexpansive square

JO - Compositio Mathematica

PY - 1970

PB - Wolters-Noordhoff Publishing

VL - 22

IS - 3

SP - 269

EP - 274

LA - eng

UR - http://eudml.org/doc/89058

ER -

## References

top- C. Bessaga [1] Every infinite-dimensiona 1 Hilbert space is diffeomorphic with its unit sphere. Bull. Acad. Polon. Sci.19 (1966), pp. 27-31. Zbl0151.17703MR193646
- M.S. Brodskii AND D.P. Milman [2] On the center of a convex set, Dokl. Acad. Nauk SSSR N.S., 59 (1948) pp. 837-840. Zbl0030.39603MR24073
- F.E. Browder [3] Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA54 (1965), pp. 1041-1044. Zbl0128.35801MR187120
- J.A. Clarcson [4] Uniformly convex spaces, Trans. Amer. Math. Soc.40 (1936), pp 396-414. Zbl0015.35604MR1501880JFM62.0460.04
- R.C. James [5] Uniformly non-square Banach spaces, Ann. of Math.80 (1964), pp. 542-550. Zbl0132.08902MR173932
- W.A. Kirk [6] A fixed point theorems for mappings which do not increase distances, Amer. Math. Monthly72 (1965) pp. 1004-1006. Zbl0141.32402MR189009
- Z. Opial [7] Lecture notes on nonexpansive and monotone mappings in Banach spaces, Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island USA (1967).

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- Krzysztof Pupka, Fixed points of periodic and firmly lipschitzian mappings in Banach spaces

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