Ravi P. Agarwal, Erdal Karapinar, Donal O'Regan and Antonio Francisco Roldán-López-de-Hierro; Fixed Point Theory in Metric Type Spaces, Cham: Springer, 2015, xvii+385 p. ISBN 978-3-319-24080-0/hbk; 978-3-319-24082-4/ebook).

Abstract

The book is devoted to fixed points in generalized metric (G-metric) spaces. A G-metric on a set X is a function G : X3 ! [0;1) satisfying the following conditions: (G1) G(x; y; z) = 0 () x = y = z; (G2) G(x; x; y) > 0) for all x; y 2 X with x 6= y; (G3) G(x; x; y) G(x; y; z) for all x; y; z 2 X with x 6= y; (G4) G(x; y; z) = G((x; y; z)) for every pemutation of x; y; z; (G5) G(x; y; z) G(x;w;w) + G(w; y; z) for all x; y; z;w 2 X :