In this paper, we study a fixed-point problem with set-valued mapping by using an algorithm based on unions of nonexpansive mappings. We show that approximate solution is reached after finite number iterations in the presence computational errors. This result extension results known literature.

in this paper, we prove some coupled coincidence point theorems for mappings with the mixedmonotone property and obtain the uniqueness of this coincidence point. then we providing useful examples in nash equilibrium.

Abstract. This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enj...

The main purpose of this paper is to study an iteration procedure for finding a common fixed point of a countable family of nonexpansive mappings in Banach spaces. We introduce a Mann type iteration procedure. Then we prove that such a sequence converges weakly to a common fixed point of a countable family of nonexpansive mappings. Moreover, we apply our result to the problem of finding a commo...

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.