Fixed point theory is one of fundamental tools of nonlinear functional analysis. Since the fixed point theory has a wide application area in almost all quantitative sciences, many authors have been working on this field. One of the impressive initial results in this direction was given by Banach 1 , known as Banach Contraction Mapping Principle. It states that each contraction in a complete met...

Recently, Choudhury and Metiya [Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of the Banach's contraction mapping, which have been studied by several authors. In this paper, we introduce the notion of $f$-weak contractions and als...

In this work, we study some new common fixed point results for generalized contractive multi-valued non-self-mappings on complete metric spaces. © 2011 Elsevier Ltd. All rights reserved.

In this paper we study the Lindley-type equation W = max{0, B − A−W}. Its main characteristic is that it is a non-increasing monotone function in its main argument W. Our main goal is to derive a closed-form expression of the steady-state distribution of W. In general this is not possible, so we shall state a sufficient condition that allows us to do so. We also examine stability issues, derive...

and Applied Analysis 3 an energy condition. Section 4 is devoted to long time behaviors of global solutions, including the existence of global fast solution and slow solution. 2. Local Existence and Uniqueness In this section, we prove the following local existence and uniqueness of the solution to 1.2 by contraction mapping principle. Theorem 2.1. For any given u0 satisfying u0 ∈ C1 α 0, s0 wi...

We survey the application of contraction mapping argments to selfsimilar (nonrandom) fractal sets, measures and functions. We review the results for selfsimilar random fractal sets and measures and show how the method and extensions also work for selfsimilar random fractal functions.

In this article, we prove the existence of a best proximity point for F contractive nonself mappings and state some results in the complete metric spaces. Also we define two kinds of F proximal contraction and extend some best proximity theorems and improve the recent results. 2010 Mathematics Subject Classification: 46N40; 47H10; 54H25; 46T99