An Algorithm with Fast Convergence Rate for Approximation of Fixed Points
Subject Areas : Fixed Point Theory and its Applications
Sara Ebrahimi
1
,
Hamid Sahebi
2
1 - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
2 - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
Keywords: Weak contraction mapping, fixed point, Rate of convergence,
Abstract :
In this paper, we introduce a new iterative algorithm and show that this algorithm canbe used to approximate fixed point of weak contraction mappings. Furthermore, we prove that thisiteration is equivalent to Mann iterative scheme and converges faster than many iterativescheme for the class of weak contraction mappings. To support the main outcome of the paper, weprovide some numerical examples and show that these examples properly exceed the class of contraction maps.