In this paper, we proved coincidence points theorems for two pairs mappings which are defined on nonempty subset in metric spaces by using condition (1.1). As application, we established a unique common fixed points theorems for these mappings by using the concept weakly compatible (R-weakly commuting) between these mappings.

In this paper, we prove the existence of common random fixed point for two random operators under general quasi contraction condition in a complete pnormed space X (with whose dual separates the point of X). Also, the wellposedness problem of random fixed points is studied. Our results essentially cover special cases.

The purpose of this paper is to introduce and study the concepts of fuzzy generalized pre-open sets, fuzzy generalized pre-closed sets and generalized pre-continuous fuzzy proper functions. Some of its properties have also been investigated. Relation between continuous fuzzy proper functions and generalized pre-continuous fuzzy proper functions has also been established.

The purpose of this paper is to prove a common fixed point(c.f.p) theorems by using conditiond (S(x), T(y)) ≤ℓ max{d(h(x), G(y)), d(h(x), S(x)), d(G(y), T(y)), d(h(x), T(y)), d(G(y), S(x))} For two pairs of mappings in p-normed space(p-n.s) and also obtain the best approximation (b.a) result. In the last part of this paper, it is proved that the fixed point (f.p) problem for these mappings is well-posed (w-p).

In this paper, firstly, we prove the existence of random coincidence points for general ϕ – weakly contraction condition under two pairs of random operators in metric spaces X, where ϕ is continuous monotone real function. As applications related common random fixed point results are proved and the well-posed random fixed point problem is studied.