Fixed Points Results via Iterates of Four Maps in ... - Semantic Scholar

Proceedings of the World Congress on Engineering 2010 Vol III WCE 2010, June 30 - July 2, 2010, London, U.K.

Fixed Points Results via Iterates of Four Maps in TVS-valued Cone Metric Spaces Muhammad Arshad and Akbar Azam Let ( E , τ ) be always a topological vector space (TVS) Abstract—: We obtain common fixed points of four mappings satisfying a contractive type condition by demonstrating the convergence of their sequence of iterates in TVS valued cone metric spaces. Our results generalize some well-known recent results in the literature.

Index Terms— contractive type mapping; non-normal cones; fixed point ; cone metric space. I. INTRODUCTION AND PRELIMINARIES Fixed point theorems are very important tools for providing evidence of the existence and uniqueness of solutions to various mathematical models (i.e., differential, integral and partial differential equations) representing phenomena happening in different fields, such as steady state temperature distribution, chemical equations, economic theories, financial analysis and biomedical research. The literature of the last four decades flourishes with results which discover fixed points of self and nonself nonlinear operators in a metric space. For most of them, their reference result is the Banach contraction theorem, which states that if X is a complete metric space and T a single valued contractive self mapping on X , then T

and P a subset of E . Then, P is called a cone whenever (i) P is closed, non-empty and P ≠ {0}, (ii) ax + by ∈ P for all x, y ∈ P and non-negative real numbers a, b , (iii) P ∩ ( − P ) = {0}. For a given cone P ⊆ E , we can define a partial ordering ≤ with respect to P by x ≤ y if and only if

y − x ∈ P. x < y will stand for x ≤ y and x ≠ y, while x