Iterative approximation to a coincidence point of two mappings

In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.

[1]  Hong-Kun Xu.  Iterative Algorithms for Nonlinear Operators , 2002 .

[2]  G. Jungck,et al.  Commuting Mappings and Fixed Points , 1976 .

[3]  V. Berinde.  COMMON FIXED POINTS OF NONCOMMUTING DISCONTINUOUS WEAKLY CONTRACTIVE MAPPINGS IN CONE METRIC SPACES , 2010 .

[4]  Michael A. Geraghty,et al.  On contractive mappings , 1973 .

[5]  Vasile Berinde,et al.  APPROXIMATING COMMON FIXED POINTS OF NONCOMMUTING ALMOST CONTRACTIONS IN METRIC SPACES , 2010 .

[6]  R. Wittmann.  Approximation of fixed points of nonexpansive mappings , 1992 .

[7]  Oana Mleşniţe,et al.  Coincidence problems for generalized contractions , 2014 .

[8]  Jocelyne Bédard,et al.  New-York, 1985 , 2005 .

[9]  J. O. Olaleru,et al.  On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators , 2010, Int. J. Math. Math. Sci..

[10]  Coincidence and common fixed point theorems for (ψ, φ) weakly contractive mappings in generalized metric spaces , 2013 .

[11]  Ulrich Kohlenbach,et al.  Applied Proof Theory - Proof Interpretations and their Use in Mathematics , 2008, Springer Monographs in Mathematics.

[12]  Ulrich Kohlenbach,et al.  Effective metastability of Halpern iterates in CAT(0) spaces , 2011, 1107.3215.

[13]  J. Heinonen.  Lectures on Analysis on Metric Spaces , 2000 .

[14]  Mujahid Abbas,et al.  Common fixed point results for noncommuting mappings without continuity in cone metric spaces , 2008 .

[15]  B. Halpern.  Fixed points of nonexpanding maps , 1967 .

[16]  Raul Machuca.  A Coincidence Theorem , 1967 .

[17]  J. Garcia-Falset,et al.  EXISTENCE AND UNIQUENESS OF SOLUTION TO SEVERAL KINDS OF DIFFERENTIAL EQUATIONS USING THE COINCIDENCE THEORY , 2015 .

[18]  J. Garcia-Falset,et al.  Fixed point theory for 1-set contractive and pseudocontractive mappings , 2013, Appl. Math. Comput..

[19]  M. Fréchet.  Sur quelques points du calcul fonctionnel , 1906 .

[20]  Wataru Takahashi,et al.  Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces , 1997 .