### On Kannan-Geraghty maps as an extension of Kannan maps

#### International Journal of Maps in Mathematics - IJMM

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 Field Value Title On Kannan-Geraghty maps as an extension of Kannan maps Creator Fogh, Fatemeh Behnamian, Sara Pashaie, Firooz Description 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. Publisher Bayram Şahin Date 2019-03-22 Type info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Format application/pdf Identifier http://www.journalmim.com/index.php/ijmm/article/view/28 Source International Journal of Maps in Mathematics - IJMM; Vol 2 No 1 (2019): International Journal of Maps in Mathematics; 1-13 2636-7467 Language eng Relation http://www.journalmim.com/index.php/ijmm/article/view/28/25 Rights Copyright (c) 2019 International Journal of Maps in Mathematics - IJMM