On Kannan-Type Contractive Mappings. (3rd October 2018)

• Record Type: Journal Article
• Authors: Garai, Hiranmoy; Dey, Lakshmi Kanta; Senapati, Tanusri
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 13(2018)
• Page Start: 1466
• Page End: 1476
• Publication Date: 2018-10-03
• Subjects: Boundedly compact set -- fixed point property -- Kannan-type mapping -- metric space -- T-orbitally compact space; 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1485157
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we consider Kannan-type contractive self-map T on a metric space ( X, d ) such thatd ( T x, T y ) < 1 2 { d ( x, T x ) + d ( y, T y ) } for all x ≠ y ∈ X and establish some new fixed point results without taking the compactness of X and also relaxing the continuity of T . Further, we anticipate a result ensuring the completeness of the space X via fixed point property of this map. Finally, we give an affirmative answer to the open question posed by J. Górnicki [ Fixed point theorems for Kannan-type mappings, J. Fixed Point Theory Appl. 2017]. Apart from these, our manuscript consists of several nontrivial examples which signify the motivation of our investigations.