FIXED POINT THEOREMS OF CONTRACTIVE MAPPINGS WITHOUT CONTINUITY AND MONOTONICITY IN ORDERED CONE b-METRIC SPACES

Adrian, Ioan, Hussain and Shah introduced ordered L-spaces and cone bmetric spaces, respectively (see [B.S. Choudhury, N. Metiya: Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134(2005), No. 2, 411-418] and [N. Hussian, M.H. Shah: KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62(2011), 1677-1684], respectively). The former obtained the unique fixed point theorems in ordered L-spaces, while the latter got some topological properties of cone b-metric spaces. Following Adrian, Ioan, Hussain and Shah, the present paper will show unique fixed point results for self-mappings which do not satisfy the continuity and monotonicity in ordered cone b-metric spaces without the assumption of normality, where the coefficient s satisfies s ≥ 1. Our main results improve and generalize some related results in the literature.