- -

Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: 11057-45289-1-PB.pdf
Tamaño: 213.9Kb
Formato: PDF
Abrir
dc.contributor.author Pant, Rajendra es_ES
dc.contributor.author Pandey, Rameshwa es_ES
dc.date.accessioned 2019-04-04T10:25:02Z
dc.date.available 2019-04-04T10:25:02Z
dc.date.issued 2019-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/118977
dc.description.abstract [EN] We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappingss in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed. 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 Reich-Suzuki type nonexpansive mapping es_ES
dc.subject Hyperbolic metric space es_ES
dc.subject Iteration process es_ES
dc.subject Nonexpansive mappings es_ES
dc.title Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces es_ES
dc.type Artículo es_ES
dc.date.updated 2019-04-04T06:30:13Z
dc.identifier.doi 10.4995/agt.2019.11057
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Pant, R.; Pandey, R. (2019). Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces. Applied General Topology. 20(1):281-295. https://doi.org/10.4995/agt.2019.11057 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2019.11057 es_ES
dc.description.upvformatpinicio 281 es_ES
dc.description.upvformatpfin 295 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 M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik 66, no. 2 (2014), 223-234. es_ES
dc.description.references R. P. Agarwal, D. O'Regan and D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79. es_ES
dc.description.references A. Amini-Harandi, M. Fakhar and H. R. Hajisharifi, Weak fixed point property for nonexpansive mappings with respect to orbits in Banach spaces, J. Fixed Point Theory Appl. 18, no. 3 (2016), 601-607. https://doi.org/10.1007/s11784-016-0310-3 es_ES
dc.description.references K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74, no. 13 (2011), 4387-4391. https://doi.org/10.1016/j.na.2011.03.057 es_ES
dc.description.references B. A. Bin Dehaish and M. A. Khamsi, Browder and Göhde fixed point theorem for monotone nonexpansive mappings, Fixed Point Theory Appl. 2016:20 (2016). https://doi.org/10.1186/s13663-016-0505-8 es_ES
dc.description.references H. Busemann, Spaces with non-positive curvature, Acta Math. 80 (1948), 259-310. https://doi.org/10.1007/BF02393651 es_ES
dc.description.references T. Butsan, S. Dhompongsa and W. Takahashi, A fixed point theorem for pointwise eventually nonexpansive mappings in nearly uniformly convex Banach spaces, Nonlinear Anal. 74, no. 5 (2011), 1694-1701. https://doi.org/10.1016/j.na.2010.10.041 es_ES
dc.description.references J. García-Falset, E. Llorens-Fuster and T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl. 375, no. 1 (2011), 185-195. https://doi.org/10.1016/j.jmaa.2010.08.069 es_ES
dc.description.references H. Fukhar-ud-din and M. A. Khamsi, Approximating common fixed points in hyperbolic spaces, Fixed Point Theory Appl. 2014:113 (2014). https://doi.org/10.1186/1687-1812-2014-113 es_ES
dc.description.references K. Goebel and M. Japón-Pineda, A new type of nonexpansiveness, Proceedings of 8-th international conference on fixed point theory and applications, Chiang Mai, 2007. es_ES
dc.description.references K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3 es_ES
dc.description.references K. Goebel, T. Sekowski and A. Stachura, Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball, Nonlinear Anal. 4, no. 5 (1980), 1011-1021. https://doi.org/10.1016/0362-546X(80)90012-7 es_ES
dc.description.references K. Goebel and W. A. Kirk, Iteration processes for nonexpansive mappings, Topological methods in nonlinear functional analysis (Toronto, Ont., 1982), Contemp. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1983, pp. 115-123. https://doi.org/10.1090/conm/021/729507 es_ES
dc.description.references K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 83, Marcel Dekker, Inc., New York, 1984. https://doi.org/10.1112/blms/17.3.293 es_ES
dc.description.references M. Gregus, Jr., A fixed point theorem in Banach space, Boll. Un. Mat. Ital. A (5) 17, no. 1 (1980), 193-198. es_ES
dc.description.references M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, english ed., Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2007, Based on the 1981 French original, With appendices by M. Katz, P. Pansu and S. Semmes, Translated from the French by Sean Michael Bates. https://doi.org/10.1007/978-0-8176-4583-0 es_ES
dc.description.references B. Gunduz and S. Akbulut, Strong convergence of an explicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces, Miskolc Math. Notes 14 (2013), no. 3, 905-913. https://doi.org/10.18514/mmn.2013.641 es_ES
dc.description.references S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59, no. 1 (1976), 65-71. https://doi.org/10.1090/S0002-9939-1976-0412909-X es_ES
dc.description.references M. A. Khamsi, On metric spaces with uniform normal structure, Proc. Amer. Math. Soc. 106, no. 3 (1989), 723-726. https://doi.org/10.1090/S0002-9939-1989-0972234-4 es_ES
dc.description.references M. A. Khamsi and A. R. Khan, Inequalities in metric spaces with applications, Nonlinear Anal. 74 (2011), no. 12, 4036-4045. https://doi.org/10.1016/j.na.2011.03.034 es_ES
dc.description.references S. H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory Appl. 2013:69 (2013), 10. https://doi.org/10.1186/1687-1812-2013-69 es_ES
dc.description.references S. H. Khan, D. Agbebaku and M. Abbas, Three step iteration process for two multivalued nonexpansive maps in hyperbolic spaces, J. Math. Ext. 10, no. 4 (2016), 87-109. es_ES
dc.description.references S. H. Khan and M. Abbas, Common fixed point results for a Banach operator pair in CAT(0) spaces with applications, Commun. Fac. Sci. Univ. Ank. S'{e}r. A1 Math. Stat. 66 (2017), no. 2, 195-204. https://doi.org/10.1501/commua1_0000000811 es_ES
dc.description.references S. H. Khan, M. Abbas and T. Nazir, Existence and approximation results for skc mappings in busemann spaces, Waves Wavelets Fractals Adv. Anal. 3 (2017), 48-60. es_ES
dc.description.references https://doi.org/10.1515/wwfaa-2017-0005 es_ES
dc.description.references S. H. Khan and H. Fukhar-ud din, Convergence theorems for two finite families of some generalized nonexpansive mappings in hyperbolic spaces, J. Nonlinear Sci. Appl. 10, no. 2 (2017), 734-743. https://doi.org/10.22436/jnsa.010.02.34 es_ES
dc.description.references A. R. Khan, H. Fukhar-ud din and M. A. A. Khan, An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl. 2012:54 (2012), 12. https://doi.org/10.1186/1687-1812-2012-54 es_ES
dc.description.references W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339-346. https://doi.org/10.1007/BF02757136 es_ES
dc.description.references W. A. Kirk, Fixed point theory for nonexpansive mappings, Fixed point theory (Sherbrooke, Que., 1980), Lecture Notes in Math., vol. 886, Springer, Berlin-New York, 1981, pp. 484-505. https://doi.org/10.1007/bfb0092201 es_ES
dc.description.references W. A. Kirk, Fixed point theorems in CAT(0) spaces and R-trees, Fixed Point Theory Appl. 2004:4 (2004), 309-316. https://doi.org/10.1155/S1687182004406081 es_ES
dc.description.references W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68, no. 12 (2008), 3689-3696. https://doi.org/10.1016/j.na.2007.04.011 es_ES
dc.description.references U. Kohlenbach, Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. Soc. 357, no. 1 (2005), 89-128. https://doi.org/10.1090/S0002-9947-04-03515-9 es_ES
dc.description.references L. Leustean, Nonexpansive iterations in uniformly convex W-hyperbolic spaces, Nonlinear analysis and optimization I. Nonlinear analysis, Contemp. Math., vol. 513, Amer. Math. Soc., Providence, RI, 2010, pp. 193-210. https://doi.org/10.1090/conm/513/10084 es_ES
dc.description.references L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J. Math. Anal. Appl. 325, no. 1 (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 E. Llorens-Fuster, Orbitally nonexpansive mappings, Bull. Austral. Math. Soc. 93, no. 3 (2016), 497-503. https://doi.org/10.1017/S0004972715001318 es_ES
dc.description.references W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510. https://doi.org/10.1090/S0002-9939-1953-0054846-3 es_ES
dc.description.references K. Menger, Untersuchungen über allgemeine metrik, Math. Ann. 100, no. 1 (1928), 75-163. https://doi.org/10.1007/BF01448840 es_ES
dc.description.references S. A. Naimpally, K. L. Singh and J. H. M. Whitfield, Fixed points in convex metric spaces, Math. Japon. 29, no. 4 (1984), 585-597. es_ES
dc.description.references A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory Appl. (2010), Art. ID 458265, 19. https://doi.org/10.1155/2010/458265 es_ES
dc.description.references M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251, no. 1 (2000), 217-229. https://doi.org/10.1006/jmaa.2000.7042 es_ES
dc.description.references R. Pant and R. Shukla, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 38, no. 2 (2017), 248-266. https://doi.org/10.1080/01630563.2016.1276075 es_ES
dc.description.references S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. 15 (1990), no. 6, 537-558. https://doi.org/10.1016/0362-546x(90)90058-o es_ES
dc.description.references Ritika and S. H. Khan, Convergence of Picard-Mann hybrid iterative process for generalized nonexpansive mappings in CAT(0) spaces, Filomat 31, no. 11 (2017), 3531-3538. https://doi.org/10.2298/FIL1711531R es_ES
dc.description.references Ritika and S. H. Khan, Convergence of RK-iterative process for generalized nonexpansive mappings in CAT(0) spaces, Asian-European Journal of Mathematics, to appear. https://doi.org/10.1142/s1793557119500773 es_ES
dc.description.references H. F. Senter and W. G. Dotson, Jr., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-380. https://doi.org/10.1090/S0002-9939-1974-0346608-8 es_ES
dc.description.references T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340, no. 2 (2008), 1088-1095. https://doi.org/10.1016/j.jmaa.2007.09.023 es_ES
dc.description.references W. Takahashi, A convexity in metric space and nonexpansive mappings. I, Kodai Math. Sem. Rep. 22 (1970), 142-149. https://doi.org/10.2996/kmj/1138846111 es_ES
dc.description.references B. S. Thakur, D. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings, Appl. Math. Comput. 275 (2016), 147-155. https://doi.org/10.1016/j.amc.2015.11.065 es_ES


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

Mostrar el registro sencillo del ítem