On multivalued f-nonexpansive maps

• Autorzy: Latif A. , Tweddle I.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove coincidence and common fixed points results for single-valued maps f and multivalued f-nonexpansive maps with star-shaped weakly compact domains in Banach spaces, which extend the theorems of [3], [6], [8] and others. Moreover weak convergence and strong convergence results for coincidence point sets have also been proved, extending'a result in [1].

Słowa kluczowe

EN

f-nonexpansive maps; Banach space; fixed points

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 1999
• Tom: Vol. 32, nr 3
• Strony: 565--574
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Latif A.

• Department of Mathematics, King Abdul Aziz University, P.O. Box 9028, Jeddah 21413, Saudi Arabia

autor

Tweddle I.

• Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, Scotland, UK

Bibliografia

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• [3] W. G. Dotson, Jr., Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. (2) 4 (1972), 408-410.
• [4] J. P. Gosses, E. Lami Dozo, Some geometric properties related to the fixed point theory for nonexpansive mappings, Pacific J. Math., 40, no. 3 (1972), 565-573.
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• [6] G. Jungck, S. Sessa, Fixed point theorems in best approximation theory, Math. Japonica 42, no. 2 (1995), 249-252.
• [7] H. Kaneko, Single-valued and multivalued f-contractions, Boll. Un. Mat. Ital., (6) 4-A (1985), 29-33.
• [8] E. Lami Dozo, Multivalued nonexpansive mappings and Opial's condition, Proc. Amer. Math. Soc., 38, no. 2 (1973), 286-292.
• [9] J. T. Markin, A fixed point theorem for set-valued mappings, Bull. Amer. Math. Soc., 74, no. 4 (1968), 639-640.
• [10] S. B. Nadler, Jr., Multivalued contraction mappings, Pacific J. Math., 30, no. 2 (1969), 475-488.
• [11] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73, no. 4 (1967), 591-597.
• [12] P. Pietramala, Convergence of approximating fixed points sets for multivalued nonexpansive mappings, Comment. Math. Univ. Carolinae 32, no. 4 (1991), 697-701.