IN THIS WORK, WITHOUT ASSUMPTIONS ON THE CONTINUITY AND THE SUBADDITIVITY OF  H, WE GIVE A SIMPLE PROOF AND A CHARACTERIZATION OF THE EXISTENCE OF CARISTI-KIRK’S PROBLEM. ALSO A SUPPLEMENTARY EXAMPLE IS GIVEN.

IN THIS PAPER WE PROVE A fixed point theorem IN COMPACT CONE METRIC SPACES BY USING IMPLICIT RELATION TECHNIQUE.

IN THIS PAPER, WE OBTAIN THE EXISTENCE OF APPROXIMATE fixed pointS theoremS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPING IN A BANACH SPACE. ALSO WE PROVE THE SETAF (T) OF APPROXIMATE fixed pointS OFT IS CLOSED AND CONVEX.

IN THE PRESENT WORK, WE EXTEND CARISTI'S fixed point theorem, EKELAND'S VARIATIONAL PRINCIPLE AND TAKAHASHI'S MAXI-MIZATION theorem TO FUZZY METRIC SPACES IN THE SENSE OF GEORGE AND VEERAMANI [A. GEORGE, P VEERAMANI. ON SOME RESULTS IN FUZZY METRIC SPACES, FUZZY SETS AND SYSTEMS. 64 (1994) 395-399]. FURTHER, A DIRECT SIMPLE PROOF OF THE EQUIVALENCES BETWEEN THESE theoremS IS PROVIDED. ALSO SOME ILLUSTRATIVE EXAMPLES ARE GIVEN.