scholarly journals Hölder’s means and fixed points for multivalued nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6531-6547
Author(s):  
Mina Dinarvand
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Recent Literature ◽  
Nonexpansive Mappings ◽  
Convergent Sequence ◽  
Normal Structure ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Conditions ◽  
Weakly Convergent Sequence Coefficient

In this paper, we show some geometric conditions on Banach spaces by considering H?lder?s means and many well known parameters namely the James constant, the von Neumann-Jordan constant, the weakly convergent sequence coefficient, the normal structure coefficient, the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings and normal structure of Banach spaces. Some of our main results improve and generalize several known results in the recent literature on this topic. We also show that some of our results are sharp.

scholarly journals Some Inequalities Concerning the Weakly Convergent Sequence Coefficient in Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-8
Author(s):  
Hongwei Jiao ◽  
Yunrui Guo
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Convergent Sequence ◽  
Normal Structure ◽  
Weakly Convergent Sequence Coefficient

We establish two inequalities concerning the weakly convergent sequence coefficient and other parameters, which enable us to obtain some sufficient conditions for normal structure.

scholarly journals On some Banach space properties sufficient for normal structure

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1305-1315 ◽  
Author(s):  
Mina Dinarvand
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Recent Literature ◽  
Nonexpansive Mappings ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Fixed Point Property ◽  
Point Property ◽  
Von Neumann

In this paper, we present some sufficient conditions for which a Banach space has normal structure and therefore the fixed point property for nonexpansive mappings in terms of the generalized James, von Neumann-Jordan, Zb?ganu constants, the Ptolemy constant and the Dom?nguez-Benavides coefficient. Our main results extend and improve some known results in the recent literature.

scholarly journals Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1285
Author(s):  
Asif Ahmad ◽  
Yuankang Fu ◽  
Yongjin Li
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Geometric Properties ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Constants

In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,▵), L2(X,▵) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,▵), L2(X,▵), and calculate the bounds of L1(X,▵) and L2(X,▵) as well as the values of L1(X,▵) and L2(X,▵) for two Banach spaces.

scholarly journals Fixed points of quasi-nonexpansive mappings

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Linear Space ◽  
Complex Plane ◽  
Normed Linear Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
The Other ◽  
Commuting Mappings ◽  
Analytic Mappings

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].

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

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.

scholarly journals On Suzuki Mappings in Modular Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 319 ◽  
Author(s):  
Andreea Bejenaru ◽  
Mihai Postolache
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Modular Spaces ◽  
New Framework

Inspired by Suzuki’s generalization for nonexpansive mappings, we define the ( C ) -property on modular spaces, and provide conditions concerning the fixed points of newly introduced class of mappings in this new framework. In addition, Kirk’s Lemma is extended to modular spaces. The main outcomes extend the classical results on Banach spaces. The major contribution consists of providing inspired arguments to compensate the absence of subadditivity in the case of modulars. The results herein are supported by illustrative examples.

scholarly journals Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xianbing Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Bounded Sets

It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.

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