The homotopic invariance for fixed points of set-valued mappings in Banach spaces

2013 ◽  
Vol 7 ◽  
pp. 2341-2348
Author(s):  
Bancha Panyanak
2020 ◽  
Vol 18 ◽  
pp. 52-59
Author(s):  
Salwa Salman Abed

  The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping  and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by  yn+1 = tn z+ (1-tn )un ,  un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces.  As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved


2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson

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].


2019 ◽  
Vol 28 (2) ◽  
pp. 191-198
Author(s):  
T. M. M. SOW

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.


2020 ◽  
Vol 29 (1) ◽  
pp. 27-36
Author(s):  
M. M. GUEYE ◽  
M. SENE ◽  
M. NDIAYE ◽  
N. DJITTE

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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