scholarly journals Fixed point theorems for a k-set contraction map on a nearly-convex subset of a locally convex space

2007 ◽  
Vol 2 ◽  
pp. 1329-1340
Author(s):  
Chi-Ming Chen ◽  
Cheng-Te Liu
Keyword(s):  
Fixed Point ◽  
Convex Subset ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Locally Convex Space ◽  
Contraction Map ◽  
Locally Convex

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.

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.

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 Some fixed-point theorems on locally convex linear topological spaces

1975 ◽  
Vol 13 (2) ◽  
pp. 241-254 ◽  
Author(s):  
E. Tarafdar
Keyword(s):  
Fixed Point ◽  
Topological Space ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Topological Spaces ◽  
The Family ◽  
Image Position ◽  
Commutative Family ◽  
Locally Convex

Let (E, τ) be a locally convex linear Hausdorff topological space. We have proved mainly the following results.(i) Let f be nonexpansive on a nonempty τ-sequentially complete, τ-bounded, and starshaped subset M of E and let (I-f) map τ-bounded and τ-sequentially closed subsets of M into τ-sequentially closed subsets of M. Then f has a fixed-point in M.(ii) Let f be nonexpansive on a nonempty, τ-sequentially compact, and starshaped subset M of E. Then f has a fixed-point in M.(iii) Let (E, τ) be τ-quasi-complete. Let X be a nonempty, τ-bounded, τ-closed, and convex subset of E and M be a τ-compact subset of X. Let F be a commutative family of nonexpansive mappings on X having the property that for some f1 ∈ F and for each x ∈ X, τ-closure of the setcontains a point of M. Then the family F has a common fixed-point in M.

scholarly journals A fixed point theorem and an application for the Cauchy problem in the scale of Banach spaces

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4387-4398 ◽  
Author(s):  
Vo Tri ◽  
Erdal Karapinar
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Convex Space ◽  
Locally Convex Space ◽  
Normed Spaces ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem ◽  
Locally Convex

The main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form (x?(t) = f[t,x(t)] + g[t,x(t)], t ? [0,?), x(0) = x0? F1, in a scale of Banach spaces {(Fs,||.||) : s ? (0, 1]}.

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