scholarly journals ORBITALLY NONEXPANSIVE MAPPINGS

2015 ◽  
Vol 93 (3) ◽  
pp. 497-503 ◽  
Author(s):  
ENRIQUE LLORENS-FUSTER
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
New Class ◽  
Nonlinear Mappings

We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals Fixed point approximation of Presic nonexpansive mappings in product of CAT (0) spaces

2016 ◽  
Vol 32 (3) ◽  
pp. 315-322
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
VASILE BERINDE ◽  
ABDUL RAHIM KHAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Control Parameters ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

We obtain a fixed point theorem for Presiˇ c nonexpansive mappings on the product of ´ CAT (0) spaces and approximate this fixed points through Ishikawa type iterative algorithms under relaxed conditions on the control parameters. Our results are new in the literature and are valid in uniformly convex Banach spaces.

scholarly journals General Higher-Order Lipschitz Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Joseph Frank Gordon
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mappings ◽  
Higher Order ◽  
Fixed Point Property ◽  
Point Property ◽  
New Class ◽  
Lipschitz Mappings ◽  
Approximate Fixed Point Property

In this paper, we introduce a new class of mappings and investigate their fixed point property. In the first direction, we prove a fixed point theorem for general higher-order contraction mappings in a given metric space and finally prove an approximate fixed point property for general higher-order nonexpansive mappings in a Banach space.

Some fixed point theorems in partial \(S_b\)-metric spaces

2018 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Koushik Sarkar ◽  
Manoranjan Singha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
New Class ◽  
Contractive Mappings ◽  
Banach Contraction

N. Souayah [10] introduced the concept of partial Sb-metric spaces. In this paper, we established a fixed point theorem for a new class of contractive mappings and a generalization of Theorem 2 from [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136, (2008), 1861-1869] in partial Sb-metric spaces. We provide an example in support of our result.

scholarly journals Reflected Backward Stochastic Differential Equations Driven by Countable Brownian Motions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Pengju Duan ◽  
Min Ren ◽  
Shilong Fei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Brownian Motions ◽  
Snell Envelope ◽  
New Class

This paper deals with a new class of reflected backward stochastic differential equations driven by countable Brownian motions. The existence and uniqueness of the RBSDEs are obtained via Snell envelope and fixed point theorem.

scholarly journals A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Marwan A. Kutbi ◽  
A. Amini-Harandi ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Contractive Mappings

We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result.

scholarly journals Another proof of the Browder–Göhde–Kirk theorem via ordering argument

2002 ◽  
Vol 65 (1) ◽  
pp. 105-107 ◽  
Author(s):  
Jacek Jachymski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Nonexpansive Mappings ◽  
Partially Ordered ◽  
Common Fixed Point Theorem

Using the Zermelo Principle, we establish a common fixed point theorem for two progressive mappings on a partially ordered set. This result yields the Browder–Göhde–Kirk fixed point theorem for nonexpansive mappings.

scholarly journals On the approximation of fixed points for a new class of generalized Berinde mappings

2016 ◽  
Vol 32 (3) ◽  
pp. 363-374
Author(s):  
BESSEM SAMET ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
New Class ◽  
Contractive Type

In this paper, we introduce a new class of operators, for which a fixed point theorem is proven. This class of mappings is very large and unifies several classes of contractive type operators from the literature, including Berinde mappings. Such fact is proven via a comparison with various metrical contractive type mappings.

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