Fixed Points and Invariant Domains of Expansive Holomorphic Maps in Complex Banach Spaces

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

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Hybrid Iteration Method for Fixed Points of Nonexpansive Mappings in Arbitrary Banach Spaces

Fixed Point Theory and Applications ◽

10.1155/2007/64306 ◽

2007 ◽

Vol 2007 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

M. O. Osilike ◽

F. O. Isiogugu ◽

P. U. Nwokoro

Keyword(s):

Fixed Points ◽

Banach Spaces ◽

Iteration Method ◽

Nonexpansive Mappings

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A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2019.02.10 ◽

2019 ◽

Vol 28 (2) ◽

pp. 191-198

Author(s):

T. M. M. SOW

Keyword(s):

Strong Convergence ◽

Fixed Points ◽

Banach Spaces ◽

Iterative Scheme ◽

Nonexpansive Mappings ◽

Mann Iteration ◽

Infinite Dimensional ◽

Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

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Explicit algorithms for J-fixed points of some non linear mappings in certain Banach spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2020.01.04 ◽

2020 ◽

Vol 29 (1) ◽

pp. 27-36

Author(s):

M. M. GUEYE ◽

M. SENE ◽

M. NDIAYE ◽

N. DJITTE

Keyword(s):

Fixed Points ◽

Banach Spaces ◽

Fixed Point Theory ◽

Maximal Monotone ◽

Point Theory ◽

Duality Mapping ◽

Monotone Mappings ◽

Normalized Duality Mapping ◽

Maximal Monotone Mappings ◽

Pseudocontractive Mappings

Let E be a real normed linear space and E∗ its dual. In a recent work, Chidume et al. [Chidume, C. E. and Idu, K. O., Approximation of zeros of bounded maximal monotone mappings, solutions of hammerstein integral equations and convex minimizations problems, Fixed Point Theory and Applications, 97 (2016)] introduced the new concepts of J-fixed points and J-pseudocontractive mappings and they shown that a mapping A : E → 2 E∗ is monotone if and only if the map T := (J −A) : E → 2 E∗ is J-pseudocontractive, where J is the normalized duality mapping of E. It is our purpose in this work to introduce an algorithm for approximating J-fixed points of J-pseudocontractive mappings. Our results are applied to approximate zeros of monotone mappings in certain Banach spaces. The results obtained here, extend and unify some recent results in this direction for the class of maximal monotone mappings in uniformly smooth and strictly convex real Banach spaces. Our proof is of independent interest.

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