Coincidence Theorems on Product FC-spaces
نویسندگان
چکیده
In 1937, Von Neumann [1] established the famous coincidence theorem. Since then, the coincidence theorem was generalized in many directions. Browder [2] first proved some basic coincidence theorems for a pair of set-valued mappings in compact setting of topological vector spaces and gave some applications to minimax inequalities and variational inequalities. Recently, Ding [3] established some new coincidence theorems for a better admissible mapping on G-convex spaces by using the technique of a continuous partition of unity. In this paper, we will generalize these coincidence theorems on FC-spaces without convexity structure.
منابع مشابه
Coincidence Point and Common Fixed Point Theorems in the Product Spaces of Quasi-ordered Metric Spaces
The main aim of this paper is to study and establish some new coincidence point and common fixed point theorems in the product spaces of complete quasi-ordered metric spaces. The fixed point theorems in the product spaces will be the special case of coincidence point theorems in the product spaces. We also show that the concept of fixed point theorems in the product spaces extends the concept o...
متن کاملCoupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illus...
متن کاملCoupled coincidence point theorems for maps under a new invariant set in ordered cone metric spaces
In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.
متن کاملBest proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
متن کاملSome Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. ...
متن کامل