Remarks on best approximations in generalized convex spaces

• Autorzy: Mitrović Z. D.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove a best approximation theorem in generalized convex spaces. As an application, we derive a result on the existence of a maximal element and a coincidence point theorem in generalized convex spaces. The results of this paper generalize some known results in the literature.

Słowa kluczowe

EN

best approximations; KKM map; G-convex space

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 2
• Strony: 181--188
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Mitrović Z. D.

• Faculty of Electrical Engineering University of Banja Luka 78000 Banja Luka Patre 5 Bosnia and Herzegovina,

Bibliografia

• [1] Border, K. C., Fixed point theorems with applications to economic and gam e theory, Cambridge University Press, Cambridge, 1985.
• [2] Espinola, R., Khamsi, M. A., Introduction to Hyperconvex Spaces, Kluwer Academic Publisher, Dordrecht, 2001.
• [3] Khamsi, M. A., KKM and Ky Fan theorems in hyperconvex metric spaces, J. Math. Anal. Appl. 204 (1996), 298-306.
• [4] Kim, I. S., Park, S., Saddle point theorems on generalized convex spaces, J. Inequal. Appl. 5 (2000), 397-405.
• [5] Lin, L. J., Applications ol a fixed point theorem in G-convex space, Nonlinear Anal. 46 (2001), 601-608.
• [6] Nikodem, K., K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódz. Mat., Łódź, 1989.
• [7] Park, S., Continuous selection theorems in generalized convex spaces, Numer. Funct. Anal. Optim. 25 (1999), 567-583.
• [8] Park, S., Fixed point theorems in hyperconvex metric spaces, Nonlinear Anal. 37 (1999), 467-472.
• [9] Park, S., Kim, H., Admissible classes of multifunction on generalized convex spaces, Proc. Colloq. Natur. Sci. Seoul Natl. Univ. 18 (1993), 1-21.
• [10] Park, S., Kim, H., Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996), 173-187.
• [11] Park, S., Kim, H., Foundations of the KKM theory on generalized convex; spaces, J. Math. Anal. Appl. 209 (1997), 551-571.
• [12] Tan, K. K., Zhang, X. L., Fixed point theorems on G-convex spaces and applications, Proc. Nonlinear Funct. Anal. Appl. 1 (1996), 1-19.
• [13] Yu, Z. T., Lin, L. J., Continuous selection and fixed point theorems, Nonlinear Anal. 52 (2003), 445-455.