Ir al contenido

Documat


Fixed point theorems for a new class of nonexpansive mappings

  • Pant, Rajendra [1] ; Shukla, Rahul [2]
    1. [1] University of Johannesburg

      University of Johannesburg

      City of Johannesburg, Sudáfrica

    2. [2] Walter Sisulu University

      Walter Sisulu University

      King Sabata Dalindyebo, Sudáfrica

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 377-390
  • Idioma: inglés
  • DOI: 10.4995/agt.2022.17359
  • Enlaces
  • Resumen
    • We consider a new class of nonlinear mappings that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We present some existence and convergence results for this class of mappings. Some illustrative examples presented herein show the generality of the obtained results.

  • Referencias bibliográficas
    • R. P. Agarwal, D. O'Regan and D. R. Sahu, Fixed point theory for Lipschitzian-typemappings with applications, volume 6 Topological Fixed...
    • K. Aoyama, S. Iemoto, F. Kohsaka and W. Takahashi, Fixed point and ergodic theoremsforλ-hybrid mappings in Hilbert spaces, J. Nonlinear Convex...
    • K. Aoyama and F. Kohsaka, Fixed point theorem forα-nonexpansive mappings in Ba-nach spaces, Nonlinear Anal. 74 (2011), 4387-4391. https://doi.org/10.1016/j.na.2011.03.057
    • D. Ariza-Ruiz, C. Hern ́andez Linares, E. Llorens-Fuster and E. Moreno-G ́alvez, Onα-nonexpansive mappings in Banach spaces, Carpathian J....
    • J. Bogin, A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad.Math. Bull. 19 (1976), 7-12. https://doi.org/10.4153/CMB-1976-002-7
    • F. E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc.Nat. Acad. Sci. U.S.A. 53 (1965), 1272-1276. https://doi.org/10.1073/pnas.53.6.1272
    • F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041- 1044. https://doi.org/10.1073/pnas.54.4.1041
    • K. Goebel and W. A. Kirk, Topics in metric fixed point theory, volume 28 Cambridge Studies in Advanced Mathematics, Cambridge University Press,...
    • D. Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251- 258. https://doi.org/10.1002/mana.19650300312
    • W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004- 1006. https://doi.org/10.2307/2313345
    • F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces,...
    • M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), 217-229. https://doi.org/10.1006/jmaa.2000.7042
    • Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-...
    • R. Pant and R. Shukla, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 38,...
    • R. Pant, R. Shukla and P. Patel, Nonexpansive mappings, their extensions and generalizations in Banach spaces, in: Metric fixed point theory...
    • 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
    • R. Shukla, R. Pant and P. Kumam, On the α-nonexpansive mapping in partially ordered hyperbolic metric spaces, J. Math. Anal. 8 (2017), 1-...
    • T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), 1088-...
    • W. Takahashi, Fixed point theorems for new nonlinear mappings in a Hilbert space, J. Nonlinear Convex Anal. 11 (2010), 79- 88.
    • E. Zeidler, Nonlinear functional analysis and its applications, I, Fixed-point theorems, Springer-Verlag, New York, 1986. https://doi.org/10.1007/978-1-4612-4838-5

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno