आईएसएसएन: 1314-3344
T. Phaneendra and K. Kumara Swamy
Let (M, ï²) be a complete metric space and f a self-map on M such that ï²(fx, fy) ï£ ï¢ï²(fx, fy) for all x, y ï X, where 0 ï£ ï¢ <1/2. Kannan proved that f has a unique fixed point p and for each x ï M the iterates f, f 2 , … will converge to p. In this paper, we extend this result to a pair of self-maps on a complete 2-metric space. Our technique is remarkable to use only elementary properties of greatest lower bound, and repeatedly employing the symmetry and the tetrahedron inequality of the 2-metric instead of routine iteration procedure. This idea was initiated for only metric spaces