On Kannan-Type Contractive Mappings

被引：15

作者：

Garai, Hiranmoy ^{[1
]}

Dey, Lakshmi Kanta ^{[1
]}

Senapati, Tanusri ^{[1
,2
]}

机构：

[1] Natl Inst Technol, Dept Math, Durgapur 713209, W Bengal, India

[2] Indian Inst Technol, Dept Math, Gauhati, India

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2018年 / 39卷 / 13期

关键词：

Boundedly compact set; fixed point property; Kannan-type mapping; metric space; T-orbitally compact space; FIXED-POINT;

D O I：

10.1080/01630563.2018.1485157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider Kannan-type contractive self-map T on a metric space (X, d) such that d(Tx,Ty)< 1/2 {d(x,Tx) + d(y,Ty)} for all x not equal y is an element of 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. Gornicki [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.

引用

页码：1466 / 1476

页数：11

共 8 条

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Gornicki, Jaroslaw
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[6] KANNAN R, 1968, BULL CALCUTTA MATH S, V60, P71
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[8] COMPLETENESS AND FIXED-POINTS
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