begin{abstract} In this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. The results present...

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two s...

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

Abstract In this work we define the concepts of coupled orbit and orbitally completeness. After then, using method Bollenbacher Hicks [8], prove some Caristi type fixed point theorems in complete metric spaces for a function P : E × → E. We also give two examples that support our results.

In this paper, we establish the existence of common coupled fixed point results for new Caristi type contraction of three covariant mappings in Bipolar metric spaces. Some interesting consequences of our results are achieved. Moreover, we give an illustration which presents the applicability of the achieved results.