nach oben

vorheriger Artikel Convergence analysis for proximal split feasibi...

nächster Artikel Adomian decomposition method for solving fragme...

Tipp

Parallel and sequential hybrid methods for a finite family of asymptotically quasi \(\phi \)-nonexpansive mappings

Zeitschrift:: Journal of Applied Mathematics and Computing > Ausgabe 1-2/2015

Autoren:: Pham Ky Anh, Dang Van Hieu

Ergänzende Inhalte

» Jetzt Zugang zum Volltext erhalten

Wichtige Hinweise

Electronic supplementary material

The online version of this article (doi:10.1007/s12190-014-0801-6) contains supplementary material, which is available to authorized users.

Abstract

In this paper we study some novel parallel and sequential hybrid methods for finding a common fixed point of a finite family of asymptotically quasi \(\phi \)-nonexpansive mappings. The results presented here modify and extend some previous results obtained by several authors.

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Jetzt einloggen Kostenlos registrieren

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 69.000 Bücher
über 500 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 58.000 Bücher
über 300 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 50.000 Bücher
über 380 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Maschinenbau + Werkstoffe

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Nur für berechtigte Nutzer zugänglich

Alber, Ya.I.: Metric and generalized projection operators in Banach spaces: properties and applications. In: Kartosator, A.G. (ed.) Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, vol. 178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50. Dekker, New York (1996)

Alber, Y.I., Ryazantseva, I.: Nonlinear Ill-Posed Problems of Monotone Type. Spinger, Dordrecht (2006) MATH

Anh, P.K., Chung, C.V.: Parallel hybrid methods for a finite family of relatively nonexpansive mappings. Numer. Funct. Anal. Optim. 35(6), 649–664 (2014)

Cioranescu, I.: Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, vol. 62 of Mathematics and Its Applications. Kluwer, Dordrecht (1990) CrossRef

Chang, S.S., Kim, J.K., Wang, X.R.: Modified block iterative algorithm for solving convex feasibility problems in Banach spaces. J. Inequal. Appl. 2010, 869684 (2010). doi: 10.1155/2010/869684

Cho, Y.J., Qin, X., Kang, S.M.: Strong convergence of the modified Halpern-type iterative algorithms in B anach spaces. An. Stiint. Univ. Ovidius Constanta Ser. Mat. 17, 51–68 (2009) MATHMathSciNet

Chang, Q.W., Yan, H.: Strong convergence of a modified Halpern-type iteration for asymptotically quasi- \(\phi \)-nonexpansive mappings. An. Univ. Ovidius Constanta Ser. Mat. 21(1), 261–276 (2013). doi: 10.2478/auom-2013-0017

Diestel, J.: Geometry of Banach Spaces—Selected Topics. Lecture Notes in Mathematics, p. 485. Springer, Berlin (1975)

Deng, W.Q.: Relaxed Halpern-type iteration method for countable families of totally quasi - \(\phi \)-asymptotically nonexpansive mappings. J. Inequal. Appl. 2013, 367 (2013). doi: 10.1186/1029-242X-2013-367

10.

Deng, W.Q.: Strong convergence to common fixed points of a countable family of asymptotically strictly quasi-pseudocontractions. Math. Probl. Eng. 2013, Article ID 752625 (2013). doi: 10.1155/2013/752625

11.

Deng, W.Q., Bai, P.: An implicit iteration process for common fixed points of two infinite families of asymptotically nonexpansive mappings in Banach spaces. J. Appl. Math. 2013 Article ID 602582 (2013)

12.

Huang, N.J., Lan, H.Y., Kim, J.K.: A new iterative approximation of fixed points for asymptotically contractive type mappings in Banach spaces. Indian J. Pure Appl. Math. 35(4), 441–453 (2004) MATHMathSciNet

13.

Kang, J., Su, Y., Zhang, X.: Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications. Nonlinear Anal. Hybrid Syst. 4, 755–765 (2010) CrossRefMATHMathSciNet

14.

Kim, J.K., Kim, C.H.: Convergence theorems of iterative schemes for a finite family of asymptotically quasi- nonexpansive type mappings in metric spaces. J. Comput. Anal. Appl. 14(6), 1084–1095 (2012) MATHMathSciNet

15.

Kimura, Y., Takahashi, W.: On a hybrid method for a family of relatively nonexpansive mappings in a Banach space. J. Math. Anal. Appl. 357, 356–363 (2009) CrossRefMATHMathSciNet

16.

Kim, T.H., Takahashi, W.: Strong convergence of modified iteration processes for relatively asymptotically nonexpansive mappings. Taiwanese J. Math. 14(6), 2163–2180 (2010) MATHMathSciNet

17.

Kim, T.H., Xu, H.K.: Strong convergence of modified Mann iterations for asymptotically mappings and semigroups. Nonlinear Anal. 64, 1140–1152 (2006) CrossRefMATHMathSciNet

18.

Kim, J.K.: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi- \(\phi \)-nonexpansive mappings. Fixed Point Theory Appl. 2011, 10 (2011)

19.

Li, Y., Liu, H.B.: Strong convergence theorems for modifying Halpern-Mann iterations for a quasi- \(\phi \)-asymptotically nonexpansive multi-valued mapping in Banach spaces. Appl. Math. Comput. 218, 6489–6497 (2012) CrossRefMathSciNet

20.

Liu, X.F.: Strong convergence theorems for a finite family of relatively nonexpansive mappings. Vietnam J. Math. 39(1), 63–69 (2011) MATHMathSciNet

21.

Matsushita, S., Takahashi, W.: A strong convergence theorem for relatively nonexpansive mappings in a Banach space. J. Approx. Theory. 134, 257–266 (2005) CrossRefMATHMathSciNet

22.

Plubtieng, S., Ungchittrakool, K.: Approximation of common fixed points for a countable family of relatively nonexpansive mappings in a Banach space and applications. Nonlinear Anal. 72, 2896–2908 (2010) CrossRefMATHMathSciNet

23.

Qin, X., Cho, Y.J., Kang, S.M., Zhou, H.: Convergence of a modified Halpern-type iteration algorithm for quasi- \(\phi \)-nonexpansive mappings. Appl. Math. Lett. 22, 1051–1055 (2009) CrossRefMATHMathSciNet

24.

Reich, S., Sabach, S.: Two strong convergence theorems for a proximal method in reflexive Banach spaces. Numer. Funct. Anal. Optim. 31, 22–44 (2010) CrossRefMATHMathSciNet

25.

Reich, S., Sabach, S.: Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces. Nonlinear Anal. 73, 122–135 (2010) CrossRefMATHMathSciNet

26.

Su, Y., Li, M., Zhang, H.: New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators. Appl. Math. Comput. 217(12), 5458–5465 (2011) CrossRefMATHMathSciNet

27.

Su, Y.F., Wang, Z.M., Xu, H.K.: Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings. Nonlinear Anal. 71, 5616–5628 (2009) CrossRefMATHMathSciNet

28.

Tang, J.F., Chang, S.S., Liu, M., Liu, J.A.: Strong convergence theorem of a hybrid projection algorithm for a family of quasi- \(\phi \)-asymptotically nonexpansive mappings. Opuscula Math. 30(3), 341–348 (2010) CrossRefMATHMathSciNet

29.

Takahashi, W., Takeuchi, Y., Kubota, R.: Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 341, 276–286 (2008) CrossRefMATHMathSciNet

30.

Takahashi, W., Zembayashi, K.: Strong convergence theorem by a new hybrid method for equilibrium p roblems and relatively nonexpansive mappings. Fixed Point Theory Appl. 2008, (2008); Article ID 528476. doi: 10.1155/2008/528476

31.

Wang, Z.M., Kumam, P.: Hybrid projection algorithm for two countable families of hemirelatively nonexpansive mappings and applications. J. Appl. Math. 2013 (2013); Article ID 524795. doi: 10.1155/2013/524795

32.

Wang, Y., Xuan, W.: Convergence theorems for common fixed points of a finite family of relatively nonexpansive mappings in banach spaces. Abstr. Appl. Anal. 2013 (2013); Article ID 259470. doi: 10.1155/2013/259470

33.

Zhao, L., Chang, S., Kim, J.K.: Mixed type iteration for total asymptotically nonexpansive mappings in hyperbolic spaces. Fixed Point Theory Appl. 2013, 353 (2013). doi: 10.1186/1687-1812-2013-353

34.

Zhou, H., Gao, X.: A strong convergence theorem for a family of quasi- \(\phi \)-nonexpansive mappings in a banach space. Fixed Point Theory Appl. 2009 (2009); Article ID 351265. doi: 10.1155/2009/351265

Titel: Parallel and sequential hybrid methods for a finite family of asymptotically quasi -nonexpansive mappings
Autoren:: Pham Ky Anh
Dang Van Hieu
Publikationsdatum: 01.06.2015
DOI: https://doi.org/10.1007/s12190-014-0801-6
Verlag: Springer Berlin Heidelberg
Zeitschrift: Journal of Applied Mathematics and Computing
Ausgabe 1-2/2015
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085

Premium Partner

Bildnachweise

Springer Professional

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Electronic supplementary material

Abstract

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2015

A note on area of lattice polygons in an Archimedean tiling

A line search filter inexact reduced Hessian method for nonlinear equality constrained optimization

Analysis of smoothing-type algorithms for the convex second-order cone programming

On Dirichlet two-point boundary value problems for the Ermakov–Painlevé IV equation

Extremal values of vertex-degree-based topological indices over graphs

Global stability analysis of HIV-1 infection model with three time delays

Premium Partner