IN THIS PAPER WE SHOW THAT SOME FIXED POINT THEOREMS FOR FUNCTIONS OF THREE AND FOUR VARIABLES ON ORDERED METRIC SPACES CAN BE REDUCED TO ONE VARIABLE FUNCTIONS' FIXED POINT THEOREMS, CONSEQUENTLY CAN BE FOLLOWED FROM WELL-KNOWN FIXED POINT THEOREMS IN THE LITERATURE.

IN THIS PAPER, WE WILL FIRST INTRODUCE THE APPROXIMATE FIXED POINT PROPERTY FOR A CYCLIC MAP T ON G-METRIC SPACE. ALSO, WE PROVE GENERAL LEMMA WHICH REGARDING APPROXIMATE FIXED POINT OF CYCLIC MAPS ON G-METRIC SPACE. USING THESE RESULTS WE PROVE DIAMETER APPROXIMATE FIXED POINT THEOREMS FOR VARIOUS TYPES OF THE WELL-KNOWN GENERALIZED CONTRACTIONS ON G-METRIC SPACE.

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.

LET X BE A COMPLEX BANACH SPACE WITH DIM X³3 AND B (X) THE ALGEBRA OF ALL BOUNDED LINEAR OPERATORS ON X. SUPPOSE F: B (X) ®B (X) IS A SURJECTIVE MAP SATISFYING THE FOLLOWING PROPERTY: (FORMULA) THEN THE FORM OF F IS CHARACTERIZED, WHERE FIX (T) IS THE SET OF ALL FIXED POINTS OF AN OPERATOR T.