A FIXED POINT THEOREM FOR NONEXPANSIVE MAPPINGS IN LOCALLY CONVEX SPACES

1985 ◽  
Vol 18 (3) ◽  
Author(s):  
Bogdan Rzepecki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

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 fixed point theorem in locally convex spaces

2010 ◽  
Vol 61 (2) ◽  
pp. 223-239 ◽  
Author(s):  
Vladimir Kozlov ◽  
Johan Thim ◽  
Bengt Ove Turesson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

On Rank One Commutators and Triangular Representations

1986 ◽  
Vol 29 (3) ◽  
pp. 268-273
Author(s):  
Tsoy-Wo Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Compact Operators ◽  
Locally Convex Spaces ◽  
Rank One ◽  
Locally Convex ◽  
Convex Spaces

AbstractStarting with the extension of Lomonosov's Lemma by Tychonoff fixed point theorem, a result of Daughtry and Kim — Pearcy-Shields on rank-one commutators is extended to the context of locally convex spaces. Non-zero diagonal coefficients, eigenvalues and simultaneous triangular representations of compact operators on locally convex spaces are studied.

scholarly journals Fixed points of upper semicontinuous mappings in locally G-convex spaces

1998 ◽  
Vol 58 (3) ◽  
pp. 469-478 ◽  
Author(s):  
George Xian-Zhi Yuan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Topological Spaces ◽  
Locally Convex Spaces ◽  
Upper Semicontinuous ◽  
Special Cases ◽  
Locally Convex ◽  
Convex Spaces

In this paper a new fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values is established in the setting of an abstract convex structure – called a locally G-convex space, which generalises usual convexity such as locally convex H-spaces, locally convex spaces (locally H-convex spaces), hyperconvex metric spaces and locally convex topological spaces. Our fixed point theorem includes corresponding Fan-Glicksberg type fixed point theorems in locally convex H-spaces, locally convex spaces, hyperconvex metric space and locally convex spaces in the existing literature as special cases.

scholarly journals Fixed point theorems for a sum of two mappings in locally convex spaces

1994 ◽  
Vol 17 (4) ◽  
pp. 681-686 ◽  
Author(s):  
P. Vijayaraju
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Locally Convex Spaces ◽  
Continuous Mappings ◽  
Asymptotically Nonexpansive ◽  
Locally Convex ◽  
Convex Spaces

Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed.

Amenability and Fixed Point Properties of Semitopological Semigroups in Modular Vector Spaces

2019 ◽  
Vol 63 (3) ◽  
pp. 692-704
Author(s):  
Khadime Salame
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Continuous Functions ◽  
Modular Space ◽  
Modular Spaces ◽  
Fixed Point Properties ◽  
Uniformly Continuous ◽  
Locally Convex

AbstractIn this paper, we initiate the study of fixed point properties of amenable or reversible semitopological semigroups in modular spaces. Takahashi’s fixed point theorem for amenable semigroups of nonexpansive mappings, and T. Mitchell’s fixed point theorem for reversible semigroups of nonexpansive mappings in Banach spaces are extended to the setting of modular spaces. Among other things, we also generalize another classical result due to Mitchell characterizing the left amenability property of the space of left uniformly continuous functions on semitopological semigroups by introducing the notion of a semi-modular space as a generalization of the concept of a locally convex space.

scholarly journals Fixed points and their approximations for asymptotically nonexpansive mappings in locally convex spaces

1995 ◽  
Vol 18 (2) ◽  
pp. 293-298 ◽  
Author(s):  
P. Vijayaraju
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Locally Convex Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Locally Convex ◽  
Convex Spaces

We construct an example that the class of asymptotically nonexpansive mappings include properly the class of nonexpansive mappings in locally convex spaces, prove a theorem on the existence of fixed points, and the convergence of the sequence of iterates to a fixed point for asymptotically nonexpansive mappings in locally convex spaces.

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.

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