A Fixed Point Theorem for Multivalued Mappings with δ-Distance. (24th July 2014)

• Record Type: Journal Article
• Authors: Acar, Özlem; Altun, Ishak
• Other Names: Kumam Poom Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-07-24
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/497092
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We mainly study fixed point theorem for multivalued mappings withδ -distance using Wardowski's technique on complete metric space. Let( X, d ) be a metric space and letB ( X ) be a family of all nonempty bounded subsets ofX . Defineδ : B ( X ) × B ( X ) → R byδ ( A, B ) = sup d ( a, b ) : a ∈ A, b ∈ B . Consideringδ -distance, it is proved that if( X, d ) is a complete metric space andT : X → B ( X ) is a multivalued certain contraction, thenT has a fixed point.