scholarly journals Fixed Point Theorems of a New Generalized Nonexpansive Mapping

2020 ◽  
Author(s):  
Shi Jie
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Point Theorems ◽  
Generalized Nonexpansive Mapping

On Asymptotically Nonexpansive Semigroups of Mappings

1970 ◽  
Vol 13 (2) ◽  
pp. 209-214 ◽  
Author(s):  
R. D. Holmes ◽  
P. P. Narayanaswami
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Commutative Semigroups ◽  
Nonexpansive Semigroups ◽  
Asymptotically Nonexpansive ◽  
Cluster Points

A selfmapping f of a metric space (X, d) is nonexpansive (ε-nonexpansive) if d(f(x), f(y)) ≤ d(x, y) for all x, y ∊ X (respectively if d(x, y) < ε). In [1], M. Edelstein proved that a nonexpansive mapping f of En admits a fixed point provided the f-closure of En (i.e. the set of all points which are cluster points of {fn(x)} for some x) is nonempty. R. D. Holmes [2] considered commutative semigroups of selfmappings of a metric space and obtained fixed point theorems for such semigroups under certain contractivity conditions.

scholarly journals Fixed Point Theorems for a New Class of Mappings in Modular Spaces Endowed with a Graph

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Nour-eddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Modular Space ◽  
New Class ◽  
Modular Spaces

In this paper, we discuss a class of mappings more general than ρ-nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph.

scholarly journals Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Approximate Fixed Point

We define a mean nonexpansive mappingTonXin the sense thatTx-Ty≤ax-y+bx-Ty,a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness theorems of fixed point.

scholarly journals Fixed-point theorems for multivalued non-expansive mappings without uniform convexity

2003 ◽  
Vol 2003 (6) ◽  
pp. 375-386 ◽  
Author(s):  
T. Domínguez Benavides ◽  
P. Lorenzo Ramírez
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Compact Convex ◽  
Contractive Mapping ◽  
Uniform Convexity ◽  
Opial Condition ◽  
The Family

LetXbe a Banach space whose characteristic of noncompact convexity is less than1and satisfies the nonstrict Opial condition. LetCbe a bounded closed convex subset ofX,KC(C)the family of all compact convex subsets ofC, andTa nonexpansive mapping fromCintoKC(C). We prove thatThas a fixed point. The nonstrict Opial condition can be removed if, in addition,Tis a1-χ-contractive mapping.

Convergence Theorems for Suzuki Generalized Nonexpansive Mapping in Banach Spaces

2021 ◽  
Vol 54 ◽  
Author(s):  
Abdulhamit Ekinci ◽  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Convergence Theorems ◽  
Approximate Fixed Point ◽  
Strong Theorems ◽  
Numerical Example ◽  
Generalized Nonexpansive Mapping

In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. \cite{Thakur}, Ullahand Arschad \cite{UA}.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

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