On Fixed Point Theorems for Mappings in a Separated Locally Convex Space

1972 ◽  
Vol 15 (4) ◽  
pp. 603-604 ◽  
Author(s):  
Cheng-Ming Lee
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Nonempty Subset ◽  
Locally Convex Space ◽  
Banach Contraction Principle ◽  
Locally Convex Spaces ◽  
Banach Contraction ◽  
Locally Convex ◽  
The Banach Contraction Principle

The Banach contraction principle has been generalized by Tan [6] to the mappings in separated locally convex spaces. We show that the result of Sehgal [5] and also of Holmes [3] can be generalized in the same way.Throughout this note, we let X be a separated locally convex space, U a base for the closed absolutely convex neighborhoods of the origin O in X, K a nonempty subset of X, and Ta mapping from K to K.

scholarly journals On some optimization problems in not necessarily locally convex space

2008 ◽  
Vol 18 (2) ◽  
pp. 167-172
Author(s):  
Ljiljana Gajic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Convex Space ◽  
Optimization Problems ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Equilibrium Existence ◽  
Cooperative Equilibrium ◽  
Locally Convex

In this note, by using O. Hadzic's generalization of a fixed point theorem of Himmelberg, we prove a non - cooperative equilibrium existence theorem in non - compact settings and a generalization of an existence theorem for non - compact infinite optimization problems, all in not necessarily locally convex spaces.

scholarly journals A note on Kakutani type fixed point theorems

2000 ◽  
Vol 24 (4) ◽  
pp. 231-235 ◽  
Author(s):  
A. R. Khan ◽  
N. Hussain ◽  
L. A. Khan
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Locally Convex Space ◽  
Space Setting ◽  
Locally Convex

We present Kakutani type fixed point theorems for certain semigroups of self maps by relaxing conditions on the underlying set, family of self maps, and the mappings themselves in a locally convex space setting.

scholarly journals Fixed-Point Theorems for θ − ϕ -Contraction in Generalized Asymmetric Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
Hamza Saffaj ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of θ -contraction and θ − ϕ -contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.

scholarly journals Some New Fixed Point Theorems in Complex ValuedG-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ing-Jer Lin ◽  
Wei-Shih Du ◽  
Qiao-Feng Zheng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
Complex Valued ◽  
The Banach Contraction Principle

Some new fixed point theorems are established in the setting of complex valuedG-metric spaces. These new results improve and generalize Kang et al.’s results, the Banach contraction principle, and some well-known results in the literature.

scholarly journals A note on fixed point theorems in metric spaces

2015 ◽  
Vol 31 (1) ◽  
pp. 127-134
Author(s):  
DARIUSZ WARDOWSKI ◽  
◽  
NGUYEN VAN DUNG ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we show that the existence of fixed points in some known fixed point theorems in the literature is a consequence of the Banach contraction principle.

FIXED POINT THEOREMS IN A LOCALLY CONVEX SPACE

1996 ◽  
Vol 19 (3-4) ◽  
pp. 505-515
Author(s):  
S. N. Mishra ◽  
S. L. Singh
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Locally Convex Space ◽  
Locally Convex

scholarly journals Fixed point theorems for nonexpansive mappings in a locally convex space

1979 ◽  
Vol 20 (2) ◽  
pp. 179-186 ◽  
Author(s):  
P. Srivastava ◽  
S.C. Srivastava
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Uniform Space ◽  
Normal Structure ◽  
Locally Convex Space ◽  
Uniform Spaces ◽  
Locally Convex

Several fixed point theorems for nonexpansive self mappings in metric spaces and in uniform spaces are known. In this context the concept of orbital diameters in a metric space was introduced by Belluce and Kirk. The concept of normal structure was utilized earlier by Brodskiĭ and Mil'man. In the present paper, both these concepts have been extended to obtain definitions of β-orbital diameter and β-normal structure in a uniform space having β as base for the uniformity. The closed symmetric neighbourhoods of zero in a locally convex space determine a base β of a compatible uniformity. For 3-nonexpansive self mappings of a locally convex space, fixed point theorems have been obtained using the concepts of β-orbital diameter and β-normal structure. These theorems generalise certain theorems of Belluce and Kirk.

scholarly journals On Some New Results in Graphical Rectangular b-Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 488
Author(s):  
Pravin Baradol ◽  
Jelena Vujaković ◽  
Dhananjay Gopal ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we provide an approach to establish the Banach contraction principle ( for the case λ ∈ [ 0 , 1 ) ) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).

scholarly journals New Fixed Point Theorems for θ ‐ ϕ -Contraction on Rectangular b -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of θ ‐ ϕ -contraction in metric spaces, introduced by Zheng et al., we present the notion of θ ‐ ϕ -contraction in b -rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.

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