Fixed point results for convex orbital nonexpansive type mappings
DOI:
https://doi.org/10.12775/TMNA.2023.047Słowa kluczowe
Fixed point, nonexpansive mapping, normal structureAbstrakt
We define some classes of generalized nonexpansive mappings under assumptions concerning the convex combinations of two consecutive points in their orbits. For these mappings, in the setting of Banach spaces that enjoy normal structure, we provide several fixed point results.Bibliografia
L.P. Belluce and W.A. Kirk, Fixed-point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141–146.
T. Domı́nguez Benavides and E. Llorens Fuster, Iterated noexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 104, DOI: 10.1007/s11784-018-0579-5.
J. Garcı́a-Falset, E. Llorens-Fuster and T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl. 375 (2011), 185–195.
K. Goebel and W.A. Kirk, Iteration processes for nonexpansive mappings, Contemp. Math. 21 (1983), 115–123.
J. Górnicki and R.K. Bisht Around averaged mappings. J. Fixed Point Theory Appl. 23 (2021), paper no. 48, 12 pp.
T.L. Hicks and B.E. Rhoades, A Banach type fixed-point theorem, Math. Japonica 24 (1979), 327–330.
W.A. Kirk, On mappings with diminishing orbital diameters, J. London Math. Soc. 44 (1969), 107–111.
W.A. Kirk and Shahzad, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. 463 (2018), 461–476.
W.A. Kirk and Shahzad, Orbital fixed point conditions in geodesic spaces, Fixed Point Theory 21 (2020), 221–38.
S. Kumar, Some fixed point theorems for iterated contraction maps, J. Appl. Funct. Anal. 10 (2015), no. 1-2, 31–39.
E. Llorens-Fuster, Orbitally nonexpansive mappings, Bull. Aust. Math. Soc. 93 (2016), 497–503.
E. Llorens-Fuster, Partially nonexpansive mappings, Advances in the Theory of Nonlinear Analysis and the Applications 6 (2022), no. 4, 565–573.
E. Llorens-Fuster and E. Moreno-Gálvez, The Fixed Point Theory for some generalized nonexpansive mappings, Abstract Appl. Anal. 2011 (2011), Art. ID 435686.
A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory Appl. (2010), Art. ID 458265, 19 pp.
A. Petruşel and G. Petruşel, Fixed point results for decreasing convex orbital operators in Hilbert spaces, J. Fixed Point Theory Appl. 23 (2021), no. 3, paper no3̇5, 10 pp.
A. Petruşel and I.A. Rus, Graphic contraction principle and applications, Mathematical Analysis and Applications, Springer Optim. Appl., vol. 154, Springer, Cham, 2019, 411–432.
O. Popescu, Fixed-point results for convex orbital operators, Demonstr. Math. 56 (2023), no. 1, dema–2022–0184.
W.C. Rheinboldt, A unified convergence theory for a class of iterative processes, SIAM J. Numer. Anal. 5 (1968), 42–63.
I.A. Rus, The method of successive approximations, Rev. Roumaine Math. Pures Appl. 17 (1972), 1433–1437.
P.V. Subrahmanyam, Remarks on some fixed-point theorems related to Banach’s contraction principle, J. Mathematical and Physical Sci. 8 (1974), 445–457; errata: 9 (1975), 195.
T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), 1088–1095.
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Prawa autorskie (c) 2024 Enrique Llorens-Fuster
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