# American Institute of Mathematical Sciences

2011, 1(3): 371-379. doi: 10.3934/naco.2011.1.371

## Strong convergence theorems with three-step iteration in star-shaped metric spaces

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

Received  April 2011 Revised  June 2011 Published  September 2011

The author considers a Noor-type three-step iterative scheme including Ishikawa-type scheme as a special case to approximate common fixed points of an infinite family of uniformly quasi-Lipschitzian mappings and an infinite family of nonexpansive mappings in star-shaped metric spaces. His results are cases of star-shaped metric space of results shown in [7].
Citation: Byung-Soo Lee. Strong convergence theorems with three-step iteration in star-shaped metric spaces. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 371-379. doi: 10.3934/naco.2011.1.371
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##### References:
 [1] Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557 [2] Farah Abou Shakra. Asymptotics of wave models for non star-shaped geometries. Discrete & Continuous Dynamical Systems - S, 2014, 7 (2) : 347-362. doi: 10.3934/dcdss.2014.7.347 [3] F. Ali Mehmeti, R. Haller-Dintelmann, V. Régnier. Dispersive waves with multiple tunnel effect on a star-shaped network. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 783-791. doi: 10.3934/dcdss.2013.6.783 [4] Zhong-Jie Han, Enrique Zuazua. Decay rates for elastic-thermoelastic star-shaped networks. Networks & Heterogeneous Media, 2017, 12 (3) : 461-488. doi: 10.3934/nhm.2017020 [5] Mike Boyle, Sompong Chuysurichay. The mapping class group of a shift of finite type. Journal of Modern Dynamics, 2018, 13: 115-145. doi: 10.3934/jmd.2018014 [6] Fuzhong Cong, Hongtian Li. Quasi-effective stability for a nearly integrable volume-preserving mapping. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1959-1970. doi: 10.3934/dcdsb.2015.20.1959 [7] Takahiro Hashimoto. Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains. Conference Publications, 2007, 2007 (Special) : 487-494. doi: 10.3934/proc.2007.2007.487 [8] Helmut Harbrecht, Thorsten Hohage. A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Inverse Problems & Imaging, 2009, 3 (2) : 353-371. doi: 10.3934/ipi.2009.3.353 [9] Gen Qi Xu, Siu Pang Yung. Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping. Networks & Heterogeneous Media, 2008, 3 (4) : 723-747. doi: 10.3934/nhm.2008.3.723 [10] Jason Metcalfe, Christopher D. Sogge. Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1589-1601. doi: 10.3934/dcds.2010.28.1589 [11] Giuseppe Maria Coclite, Carlotta Donadello. Vanishing viscosity on a star-shaped graph under general transmission conditions at the node. Networks & Heterogeneous Media, 2020, 15 (2) : 197-213. doi: 10.3934/nhm.2020009 [12] Fabrizio Colombo, Irene Sabadini, Frank Sommen. The inverse Fueter mapping theorem. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1165-1181. doi: 10.3934/cpaa.2011.10.1165 [13] John Banks. Topological mapping properties defined by digraphs. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 83-92. doi: 10.3934/dcds.1999.5.83 [14] Mads Kyed. On a mapping property of the Oseen operator with rotation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315 [15] T. Aaron Gulliver, Masaaki Harada, Hiroki Miyabayashi. Double circulant and quasi-twisted self-dual codes over $\mathbb F_5$ and $\mathbb F_7$. Advances in Mathematics of Communications, 2007, 1 (2) : 223-238. doi: 10.3934/amc.2007.1.223 [16] Zhengxin Zhou. On the Poincaré mapping and periodic solutions of nonautonomous differential systems. Communications on Pure & Applied Analysis, 2007, 6 (2) : 541-547. doi: 10.3934/cpaa.2007.6.541 [17] Ryan Alvarado, Irina Mitrea, Marius Mitrea. Whitney-type extensions in quasi-metric spaces. Communications on Pure & Applied Analysis, 2013, 12 (1) : 59-88. doi: 10.3934/cpaa.2013.12.59 [18] W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 [19] Pietro Baldi. Quasi-periodic solutions of the equation $v_{t t} - v_{x x} +v^3 = f(v)$. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 883-903. doi: 10.3934/dcds.2006.15.883 [20] Fernando Alcalde Cuesta, Ana Rechtman. Minimal Følner foliations are amenable. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 685-707. doi: 10.3934/dcds.2011.31.685

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