ON KANNAN-GERAGHTY MAPS AS AN EXTENSION OF KANNAN MAPS
(2019) In International Journal of Maps in Mathematics 2(1). p.1-13- Abstract
- Extending the concept of weakly Kannan maps on metric spaces, we study the maps as $f:X\rightarrow X$ on a metric space $(X, d)$ satisfying condition $d(f(x), f(y)) \leq (1/2)\beta(d(x, y))[d(x ,f(x)) + d(y, f(y))]$ for every $x, y\in X$ and a function $\beta: [0, \infty)\rightarrow [0,1)$ where for every sequence $t=\{t_n\}$ of non-negative real numbers satisfying $\beta(t_n)\rightarrow 1,$ while $t_n\rightarrow 0$. Such a map is named the Kannan-Geraghty map because of its relation to weakly Kannan map and Geraghty contraction. Firstly, we show that our new condition is different from weakly Kannan condition. Having proven the fixed point theorem, we present two useful results on Kannan-Geraghty maps. Also, we illustrate some examples of... (More)
- Extending the concept of weakly Kannan maps on metric spaces, we study the maps as $f:X\rightarrow X$ on a metric space $(X, d)$ satisfying condition $d(f(x), f(y)) \leq (1/2)\beta(d(x, y))[d(x ,f(x)) + d(y, f(y))]$ for every $x, y\in X$ and a function $\beta: [0, \infty)\rightarrow [0,1)$ where for every sequence $t=\{t_n\}$ of non-negative real numbers satisfying $\beta(t_n)\rightarrow 1,$ while $t_n\rightarrow 0$. Such a map is named the Kannan-Geraghty map because of its relation to weakly Kannan map and Geraghty contraction. Firstly, we show that our new condition is different from weakly Kannan condition. Having proven the fixed point theorem, we present two useful results on Kannan-Geraghty maps. Also, we illustrate some examples of Kannan-Graghty map having interesting properties. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/e8029c06-1144-4870-b3df-062fdcb86ec6
- author
- Fogh, Fatemeh ; Behnamian, Sara LU and Pashaei, Firooz
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- keywords
- Weakly Kannan map, proximal contraction, Geraghty contraction, Fixed point
- in
- International Journal of Maps in Mathematics
- volume
- 2
- issue
- 1
- pages
- 1 - 13
- external identifiers
-
- scopus:85117406198
- ISSN
- 2636-7467
- language
- English
- LU publication?
- no
- id
- e8029c06-1144-4870-b3df-062fdcb86ec6
- alternative location
- https://www.journalmim.com/index.php/journalMIM/article/view/28
- date added to LUP
- 2023-05-04 16:19:16
- date last changed
- 2024-01-24 04:03:15
@article{e8029c06-1144-4870-b3df-062fdcb86ec6,
abstract = {{Extending the concept of weakly Kannan maps on metric spaces, we study the maps as $f:X\rightarrow X$ on a metric space $(X, d)$ satisfying condition $d(f(x), f(y)) \leq (1/2)\beta(d(x, y))[d(x ,f(x)) + d(y, f(y))]$ for every $x, y\in X$ and a function $\beta: [0, \infty)\rightarrow [0,1)$ where for every sequence $t=\{t_n\}$ of non-negative real numbers satisfying $\beta(t_n)\rightarrow 1,$ while $t_n\rightarrow 0$. Such a map is named the Kannan-Geraghty map because of its relation to weakly Kannan map and Geraghty contraction. Firstly, we show that our new condition is different from weakly Kannan condition. Having proven the fixed point theorem, we present two useful results on Kannan-Geraghty maps. Also, we illustrate some examples of Kannan-Graghty map having interesting properties.}},
author = {{Fogh, Fatemeh and Behnamian, Sara and Pashaei, Firooz}},
issn = {{2636-7467}},
keywords = {{Weakly Kannan map, proximal contraction, Geraghty contraction, Fixed point}},
language = {{eng}},
number = {{1}},
pages = {{1--13}},
series = {{International Journal of Maps in Mathematics}},
title = {{ON KANNAN-GERAGHTY MAPS AS AN EXTENSION OF KANNAN MAPS}},
url = {{https://www.journalmim.com/index.php/journalMIM/article/view/28}},
volume = {{2}},
year = {{2019}},
}