2014, 4(4): 287-293. doi: 10.3934/naco.2014.4.287

Strong convergence of an implicit iteration process for a finite family of Lipschitz $\phi -$uniformly pseudocontractive mappings in Banach spaces

1. 

Department of Mathematics, Kyungsung University, Busan 608-736, South Korea

2. 

Department of Mathematics, Lahore Leads University, Lahore, Pakistan

Received  September 2013 Revised  September 2014 Published  December 2014

The purpose of this paper is to establish a strong convergence of an implicit iteration process to a common fixed point for a finite family of Lipschitz $\phi-$uniformly pseudocontractive mappings in real Banach spaces. The results presented here improve and extend the corresponding results in [2, 4, 6] and the consecutive remark explains in details about the facts.
Citation: B. S. Lee, Arif Rafiq. Strong convergence of an implicit iteration process for a finite family of Lipschitz $\phi -$uniformly pseudocontractive mappings in Banach spaces. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 287-293. doi: 10.3934/naco.2014.4.287
References:
[1]

F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space,, J. Math. Anal., 20 (1967), 197.   Google Scholar

[2]

R. Chen, P. K. Lin and Y. Dong, An approximation method for strictly pseudocontractive mappings,, Nonlinear Analysis (TMA), 64 (2006), 2527.  doi: 10.1016/j.na.2005.08.031.  Google Scholar

[3]

C. Moore and B. V. C. Nnoli, Iterative solution of nonlinear equations involving set-valued uniformly accretive operators,, Computers Math. Applic, 42 (2001), 131.  doi: 10.1016/S0898-1221(01)00138-9.  Google Scholar

[4]

M. O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps,, J. Math. Anal., 294 (2004), 73.  doi: 10.1016/j.jmaa.2004.01.038.  Google Scholar

[5]

H. K. Xu, Inequality in Banach spaces with applications,, Nonlinear Anal., 16 (1991), 1127.  doi: 10.1016/0362-546X(91)90200-K.  Google Scholar

[6]

H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings,, Numer. Funct. Anal., 22 (2001), 767.  doi: 10.1081/NFA-100105317.  Google Scholar

show all references

References:
[1]

F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space,, J. Math. Anal., 20 (1967), 197.   Google Scholar

[2]

R. Chen, P. K. Lin and Y. Dong, An approximation method for strictly pseudocontractive mappings,, Nonlinear Analysis (TMA), 64 (2006), 2527.  doi: 10.1016/j.na.2005.08.031.  Google Scholar

[3]

C. Moore and B. V. C. Nnoli, Iterative solution of nonlinear equations involving set-valued uniformly accretive operators,, Computers Math. Applic, 42 (2001), 131.  doi: 10.1016/S0898-1221(01)00138-9.  Google Scholar

[4]

M. O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps,, J. Math. Anal., 294 (2004), 73.  doi: 10.1016/j.jmaa.2004.01.038.  Google Scholar

[5]

H. K. Xu, Inequality in Banach spaces with applications,, Nonlinear Anal., 16 (1991), 1127.  doi: 10.1016/0362-546X(91)90200-K.  Google Scholar

[6]

H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings,, Numer. Funct. Anal., 22 (2001), 767.  doi: 10.1081/NFA-100105317.  Google Scholar

[1]

Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020320

[2]

Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020049

[3]

Soniya Singh, Sumit Arora, Manil T. Mohan, Jaydev Dabas. Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020103

[4]

Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 27-43. doi: 10.3934/naco.2020013

[5]

Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020465

[6]

Lingwei Ma, Zhenqiu Zhang. Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 537-552. doi: 10.3934/dcds.2020268

[7]

Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018

[8]

Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2021, 17 (1) : 357-368. doi: 10.3934/jimo.2019115

[9]

Giulia Cavagnari, Antonio Marigonda. Attainability property for a probabilistic target in wasserstein spaces. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 777-812. doi: 10.3934/dcds.2020300

[10]

Alessandro Carbotti, Giovanni E. Comi. A note on Riemann-Liouville fractional Sobolev spaces. Communications on Pure & Applied Analysis, 2021, 20 (1) : 17-54. doi: 10.3934/cpaa.2020255

[11]

Federico Rodriguez Hertz, Zhiren Wang. On $ \epsilon $-escaping trajectories in homogeneous spaces. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 329-357. doi: 10.3934/dcds.2020365

[12]

Noah Stevenson, Ian Tice. A truncated real interpolation method and characterizations of screened Sobolev spaces. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5509-5566. doi: 10.3934/cpaa.2020250

[13]

Giulia Luise, Giuseppe Savaré. Contraction and regularizing properties of heat flows in metric measure spaces. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 273-297. doi: 10.3934/dcdss.2020327

[14]

Justin Holmer, Chang Liu. Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 215-242. doi: 10.3934/cpaa.2020264

 Impact Factor: 

Metrics

  • PDF downloads (39)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]