undefined

undefined

doi:undefined

https://doi.org/10.22771/nfaa.2021.26.01.12

BEST APPROXIMATIONS FOR MULTIMAPS ON ABSTRACT CONVEX SPACES

Feb 24, 2021
Nonlinear functional analysis and applications
Sehie Park

Listen

Abstract

Translate Article

Take Notes

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumban, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrovic-Hussain-Sen-Radenovic on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

Similar Papers

Research Article
254
10.1016/0022-247x(78)90222-6

Approximate selections, best approximations, fixed points, and invariant sets

Jan 1, 1978
Journal of Mathematical Analysis and Applications
Simeon Reich

Approximate selections, best approximations, fixed points, and invariant sets

Research Article
81
10.1016/j.jmaa.2004.06.047

Coincidence and fixed points for hybrid strict contractions

Sep 3, 2004
Journal of Mathematical Analysis and Applications
Tayyab Kamran

Coincidence and fixed points for hybrid strict contractions

Research Article
3
10.1006/jath.1996.0014

Random Approximations and Fixed Point Theorems

Feb 1, 1996
Journal of Approximation Theory
Xian-Zhi Yuan + 2 more

Random Approximations and Fixed Point Theorems

Research Article
17
10.1186/1687-1812-2013-61

Demiclosedness principle and approximation theorems for certain classes of multivalued mappings in Hilbert spaces

Mar 18, 2013
Fixed Point Theory and Applications
Felicia O Isiogugu

We prove weak and strong convergence theorems and the demiclosedness property for classes of multivalued mappings T such that is not nonexpansive, where . Thus our results extend and improve the results on multivalued and single-valued mappings in the contemporary literature. MSC:47H10, 54H25.

Research Article
4
10.1186/1029-242x-2014-320

Fixed point theorems in "Equation missing" spaces with applications

Aug 21, 2014
Journal of Inequalities and Applications
Haishu Lu + 3 more

In this paper, noncompact CAT ( 0 ) versions of the Fan-Browder fixed point theorem are established. As applications, we obtain new minimax inequalities, a saddle point theorem, a fixed point theorem for single-valued mappings, best approximation theorems, and existence theorems of φ-equilibrium points for multiobjective noncooperative games in the setting of noncompact CAT ( 0 ) spaces. These results generalize many well-known theorems in the literature. MSC:91A10, 47H04, 47H10, 54H25.