This paper presents some results concerning the Generalized Banach Contraction Principle: In a complete metric space X if for some N ≥ 1 and 0 < M < 1 the mapping T : X → X satisfies min{d(T^j x,T^j y), 1 ≤ j ≤ N} ≤ Md(x, y) for any x, y ∈ X , then T has a unique fixed point. In some special cases, the above constant M can be replaced by a continuous, non- -increasing function 0 ≤ φ (d(x, y)) ≤ 1 such that φ (t) =1 if, and only if, t = 0.

This paper presents some results concerning the Generalized Banach Contraction Principle: In a complete metric space X if for some N ≥ 1 and 0 < M < 1 the mapping T : X → X satisfies min{d(T^j x,T^j y), 1 ≤ j ≤ N} ≤ Md(x, y) for any x, y ∈ X , then T has a unique fixed point. In some special cases, the above constant M can be replaced by a continuous, non- -increasing function 0 ≤ φ (d(x, y)) ≤ 1 such that φ (t) =1 if, and only if, t = 0.