scholarly journals Fixed point theorem for pα-nonexpansive wrt orbits in locally convex space

2020 ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Convex Space ◽  
Locally Convex Space ◽  
Locally Convex

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 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]}.

scholarly journals On some theorems of Tarafdar

1976 ◽  
Vol 15 (2) ◽  
pp. 213-221
Author(s):  
S.A. Husain ◽  
V.M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Locally Convex ◽  
Common Fixed Point Theorem

In a recent paper (Bull. Austral. Math. Soc. 13 (1975), 241–245), Tarafdar has considered nonexpansive self mappings on a subset X of a locally convex vector space E and proved an extension to E of a theorem of Göhde. The purpose of this paper is to show that the condition f: X → X, in Göhde-Tarafdar's Theorem in the above paper, may be weakened to f: X → E with f(∂X) ⊆ X. As a consequence, it is further shown that an extension to E of a well-known common fixed point theorem of Belluce and Kirk due to Tarafdar remains true on domains that are not necessarily bounded or quasi-complete.

scholarly journals An extension of a theorem of Sahab, Khan, and Sessa

2001 ◽  
Vol 27 (11) ◽  
pp. 701-706 ◽  
Author(s):  
A. R. Khan ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Invariant Approximation ◽  
Recent Theorem ◽  
Locally Convex ◽  
Convex Spaces

A fixed point theorem of Fisher and Sessa is generalized to locally convex spaces and the new result is applied to extend a recent theorem on invariant approximation of Sahab, Khan, and Sessa.

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.

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