- -

A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: 10635-45282-1-PB.pdf
Tamaño: 268.0Kb
Formato: PDF
Abrir
dc.contributor.author Izuchukwu, C. es_ES
dc.contributor.author Aremu, K. O. es_ES
dc.contributor.author Mebawondu, A. A. es_ES
dc.contributor.author Mewomo, O. T. es_ES
dc.date.accessioned 2019-04-04T09:38:52Z
dc.date.available 2019-04-04T09:38:52Z
dc.date.issued 2019-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/118970
dc.description.abstract [EN] The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Equilibrium problems es_ES
dc.subject Monotone bifunctions es_ES
dc.subject Variational inequalities es_ES
dc.subject Convex feasibility problems es_ES
dc.subject Minimization problems es_ES
dc.subject Viscosity iterations es_ES
dc.subject CAT(0) space es_ES
dc.title A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space es_ES
dc.type Artículo es_ES
dc.date.updated 2019-04-04T06:29:56Z
dc.identifier.doi 10.4995/agt.2019.10635
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Izuchukwu, C.; Aremu, KO.; Mebawondu, AA.; Mewomo, OT. (2019). A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space. Applied General Topology. 20(1):193-210. https://doi.org/10.4995/agt.2019.10635 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2019.10635 es_ES
dc.description.upvformatpinicio 193 es_ES
dc.description.upvformatpfin 210 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 20
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.description.references K. O. Aremu, C. Izuchukwu, G. C. Ugwunnadi and O. T. Mewomo, On the proximal point algorithm and demimetric mappings in CAT(0) spaces, Demonstr. Math. 51 (2018), 277-294. https://doi.org/10.1515/dema-2018-0022 es_ES
dc.description.references M. Bacák, The proximal point algorithm in metric spaces, Israel J. Math. 194 (2013), 689-701. https://doi.org/10.1007/s11856-012-0091-3 es_ES
dc.description.references M. Bacák and S. Riech, The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces, J. Fixed Point Theory Appl. 16 (2014), 189-202. https://doi.org/10.1007/s11784-014-0202-3 es_ES
dc.description.references I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Alexandrov spaces, Geom. Dedicata 133 (2008), 195-218. https://doi.org/10.1007/s10711-008-9243-3 es_ES
dc.description.references M. Bianchi and S. Schaible, Generalized monotone bifunctions and equilibrium problems, J. Optim Theory Appl. 90 (1996), 31-43. https://doi.org/10.1007/BF02192244 es_ES
dc.description.references Bridson and A. Haefliger, Metric spaces of nonpositive curvature, Springer-Verlag, Berlin, Heidelberg, New York, 1999. es_ES
dc.description.references F. Bruhat and J. Tits, Groupes réductifs sur un corp local, I. Donneés Radicielles Valuées, Institut des Hautes Études Scientifiques 41 (1972). https://doi.org/10.1007/bf02715544 es_ES
dc.description.references P. Chaoha and A. Phon-on, A note on fixed point sets in CAT(0) spaces, J. Math. Anal. Appl. 320, no. 2 (2006), 983-987. https://doi.org/10.1016/j.jmaa.2005.08.006 es_ES
dc.description.references V. Colao, G. López, G. Marino, V. Martín-Márquez, Equilibrium problems in Hadamard manifolds, J. Math. Anal. Appl. 388 (2012), 61-77. https://doi.org/10.1016/j.jmaa.2011.11.001 es_ES
dc.description.references P. L. Combetes and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005), 117-136. es_ES
dc.description.references H. Dehghan and J. Rooin, Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces, arXiv:1410.1137v1[math.FA]2014. es_ES
dc.description.references S. Dhompongsa, W. A. Kirk and B. Sims, Fixed points of uniformly Lipschitzian mappings, Nonlinear Anal. 64, no. 4 (2006), 762-772. https://doi.org/10.1016/j.na.2005.09.044 es_ES
dc.description.references S. Dhompongsa and B. Panyanak, On △-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 56 (2008), 2572-2579. https://doi.org/10.1016/j.camwa.2008.05.036 es_ES
dc.description.references J. N. Ezeora and C. Izuchukwu, Iterative approximation of solution of split variational inclusion problems, Filomat, to appear. es_ES
dc.description.references K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry and nonexpansive mappings, Marcel Dekker, New York, (1984). es_ES
dc.description.references A. N. Iusem, G. Kassay and W. Sosa, On certain conditions for the existence of solutions of equilibrium problems, Math. Program., Ser. B 116 (2009), 259-273. https://doi.org/10.1007/s10107-007-0125-5 es_ES
dc.description.references C. Izuchukwu, G. C. Ugwunnadi, O. T. Mewomo, A. R. Khan and M. Abbas, Proximal-type algorithms for split minimization problem in P-uniformly convex metric spaces, Numer. Algor., to appear. https://doi.org/10.1007/s11075-018-0633-9 es_ES
dc.description.references B. A. Kakavandi, Weak topologies in complete CAT(0) metric spaces, Proc. Amer. Math. Soc. 141, no. 3 (2013), 1029-1039. https://doi.org/10.1090/S0002-9939-2012-11743-5 es_ES
dc.description.references H. Khatibzadeh and S. Ranjbar, Monotone operators and the proximal point algorithm in complete CAT(0) metric spaces, J. Aust. Math Soc. 103, no. 1 (2017), 70-90. https://doi.org/10.1017/S1446788716000446 es_ES
dc.description.references H. Khatibzadeh and S. Ranjbar, A variational inequality in complete CAT(0) spaces, J. Fixed Point Theory Appl. 17 (2015), 557-574. https://doi.org/10.1007/s11784-015-0245-0 es_ES
dc.description.references W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), 3689-3696. https://doi.org/10.1016/j.na.2007.04.011 es_ES
dc.description.references P. Kumam and P. Chaipunya, Equilibrium problems and proximal algorithms in Hadamard spaces, arXiv: 1807.10900v1 [math.oc]. es_ES
dc.description.references L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J. Math. Anal. Appl. 325 (2007), 386-399. https://doi.org/10.1016/j.jmaa.2006.01.081 es_ES
dc.description.references T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976), 179-182. https://doi.org/10.1090/S0002-9939-1976-0423139-X es_ES
dc.description.references B. Martinet, Régularisation d'Inéquations Variationnelles par approximations successives, Rev.Francaise d'Inform. et de Rech. Opérationnelle 3 (1970), 154-158. https://doi.org/10.1051/m2an/197004r301541 es_ES
dc.description.references M. A. Noor and K. I. Noor, Some algorithms for equilibrium problems on Hadamard manifolds, J. Inequal. Appl. 2012:230, 8 pp. https://doi.org/10.1186/1029-242x-2012-230 es_ES
dc.description.references C. C. Okeke and C. Izuchukwu, A strong convergence theorem for monotone inclusion and minimization problems in complete CAT(0) spaces, Optimization Methods and Software, to appear. es_ES
dc.description.references https://doi.org/10.1080/10556788.2018.1472259 es_ES
dc.description.references O. K. Oyewole, L. O Jolaoso, C. Izuchukwu and O. T. Mewomo, On approximation of common solution of finite family of mixed equilibrium problems involving μ−α relaxed monotone mapping in a Banach space, U. P. B. Sci. Bull., Series A, to appear. es_ES
dc.description.references S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. 15 (1990), 537-558. https://doi.org/10.1016/0362-546X(90)90058-O es_ES
dc.description.references R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14 (1976), 877-898. https://doi.org/10.1137/0314056 es_ES
dc.description.references S. Saejung, Halpern's iteration in CAT(0) spaces, Fixed Point Theory Appl. 2010, Art. ID 471781, 13 pp. es_ES
dc.description.references Y. Song and X. Liu, Convergence comparison of several iteration algorithms for the common fixed point problems, Fixed Point Theory Appl. 2009, Art. ID 824374, 13 pp. https://doi.org/10.1155/2009/824374 es_ES
dc.description.references R. Suparatulatorn, P. Cholamjiak and S. Suantai, On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces, Optim. Methods and Software 32 (2017), 182-192. https://doi.org/10.1080/10556788.2016.1219908 es_ES
dc.description.references T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl. 1 (2005), 103-123. https://doi.org/10.1155/FPTA.2005.103 es_ES
dc.description.references J. Tang, Viscosity approximation methods for a family of nonexpansive mappings in CAT(0) Spaces, Abstr. Appl. Anal. 2014, Art. ID 389804, 9 pages. G. C. Ugwunnadi, C. Izuchukwu and O. T. Mewomo, Strong convergence theorem for monotone inclusion problem in CAT(0) spaces, Afr. Mat., to appear. es_ES
dc.description.references G. C. Ugwunnadi, C. Izuchukwu and O. T. Mewomo, Strong convergence theorem for monotone inclusion problem in CAT(0) spaces, Afr. Mat., to appear. https://doi.org/10.1007/s13370-018-0633-x es_ES
dc.description.references R. Wangkeeree and P. Preechasilp, Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces, J. Inequal. Appl. 2013, Art. ID 93. https://doi.org/10.1186/1029-242X-2013-93 es_ES
dc.description.references H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. 66, no. 1 (2002), 240-256. https://doi.org/10.1112/S0024610702003332 es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem