Best proximity point theorems via fixed point theorems for multivalued mappings

Fixexd point theory and applications

Satit Saejung¹  Pinya Ardsalee¹ 

[1] Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand

关键词: best proximity point;    multivalued mapping;    metric space;    47H10;    47H09;    54E50;   

DOI  :  10.1186/s13663-016-0516-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

It is well known that the concept of a best proximity point includes that of a fixed point as a special case. In this paper, we show that the best proximity point theorems of Basha and Shahzad (Fixed Point Theory Appl. 2012:42, 2012) and of Fernández-León (J. Nonlinear Convex Anal. 15(2):313-324, 2014) can be regarded as a fixed point theorem for multivalued mappings which is modified as regards the results of Mizoguchi and Takahashi (J. Math. Anal. Appl. 141(1):177-188, 1989) and of Kada et al. (Math. Jpn. 44(2):381-391, 1996).

【 授权许可】

CC BY