Abstract
In this paper we investigate the existence and uniqueness of common ï¬xed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.
Highlights
Where opt represent sup. or inf., x, y denote the state and decicion vectors respectively, T stands for the transformation of the process and f (x) represents the optimal return function with the initial state x.Afterwards, the existence and uniqueness of fixed point solutions for several classes of contractive mappings and functional equations studied by many investigators such as Bhakta and Mitra [5], Liu [15], Liu and ume [20], Pathak and Fisher [21], Baskaran and Subhramanyam [1] and others
Ray [22] proved two common fixed point theorems for three self mappings f,g and h in the complete metric space using the following contractive condition: d(f x, gy) ≤ d(hx, hy) − w(d(hx, hy)), ∀x, y ∈ X
The aim of this paper is to provide the sufficient conditions for the existence and uniqueness of common fixed point for the following type of contractive mappings metric space (X, d)
Summary
Bellman and Lee [3] first introduced the basic form of the functional equations in dynamic programming is as follows:. Ray [22] proved two common fixed point theorems for three self mappings f ,g and h in the complete metric space using the following contractive condition: d(f x, gy) ≤ d(hx, hy) − w(d(hx, hy)), ∀x, y ∈ X (2). Further Liu[15] established common fixed point theorem and introduced a class of mappings in a complete metric space as follows: d(f x, gy) ≤ max{d(hx, hy), d(hx, f x), d(hy, gy)} − w(max{d(hx, hy), d(hx, f x), d(hy, gy)}). Recall that the notion of orbitally complete metric space and orbitally continuous mapping were introduced by Ciric [9]. These definitions were extended to the case of two or three mappings by Sastry et al.[12]. We give respective definitions for pairs of mappings given in literature
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