Let A and B be nonempty subsets of a metric space X and also T :for some > 0. We call pair A, B an approximate best proximity pair. In this paper, definitions of approximate best proximity pair for a map and two maps, their diameters, T -minimizing a sequence are given in a metric space.

We define approximate fixed point and fuzzy diameter in fuzzy norm spaces. We prove theorems for various types of well-known generalized contractions on fuzzy norm spaces with the use of two general lemmas that are given regarding approximate fixed points of operators on fuzzy norm spaces.

Abstract. We consider completely norm space X, and define ε−fixed point for Tα maps, and obtain some sufficient and necessary conditions on that, we also obtain some sufficient and necessary theorems on ε−fixed point for two maps.

We �nd a common element of the set of �xed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. en, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and �xed points.

We consider the partial metric on a set X, define -fixed point for maps, and obtain some sufficient and necessary conditions on that, also we obtain some sufficient and necessary theorems on -fixed point.