scholarly journals Fixed point theorems in minimal generalized convex spaces

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 165-176 ◽  
Author(s):  
Rahmat Darzi ◽  
Rostamian Delavar ◽  
Mehdi Roohi
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Fixed Point Theorem ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Kkm Principle ◽  
Generalized Convex Space ◽  
Ky Fan ◽  
Equilibrium Theorem ◽  
Convex Spaces

This paper deals with coincidence and fixed point theorems in minimal generalized convex spaces. By establishing a kind of KKM Principle in minimal generalized convex space, we obtain some results on coincidence point and fixed point theorems. Generalized versions of Ky Fan?s lemma, Fan-Browder fixed point theorem, Nash equilibrium theorem and some Urai?s type fixed point theorems in minimal generalized convex spaces are given.

scholarly journals The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Generalized Contraction ◽  
Common Fixed Point Theorems

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

Some Fixed Point Theorems in Metrically Convex Spaces

2000 ◽  
Vol 7 (3) ◽  
pp. 523-530 ◽  
Author(s):  
M. S. Khan ◽  
H. K. Pathak ◽  
M. D. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Convex Metric Space ◽  
Convex Spaces

Abstract A fixed point theorem is proved in a complete metrically convex metric space. Our result generalizes the theorems of Assad [Tamkang J. Math. 7: 91–94, 1976] and Chatterjea [C.R. Acad., Bulgare Sci. 25: 727–730, 1972].

scholarly journals Coincidences and fixed points in locally G-convex spaces

1999 ◽  
Vol 59 (2) ◽  
pp. 297-304 ◽  
Author(s):  
P.J. Watson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Convex Spaces

A new coincidence point theorem is proved for a pair of multivalued mappings operating between G-convex spaces. From this theorem, a generalisation of the classical Fan-Glicksberg fixed point theorem is established.

scholarly journals The KKM maps and fixed point theorems in convex spaces

2003 ◽  
Vol 34 (2) ◽  
pp. 169-174
Author(s):  
Polly W. Sy ◽  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Kkm Theorem ◽  
Approximate Fixed Point ◽  
Kkm Maps ◽  
New Form ◽  
Convex Spaces

From a general form of the celebrated Knaster--Kuratowski--Mazurkiewicz (simply, KKM) theorem, we deduce a new form of the Fan--Browder fixed point theorem, an approximate fixed point theorem, and the Himmelberg fixed point theorem.

scholarly journals On some fixed point theorems

1989 ◽  
Vol 12 (1) ◽  
pp. 61-64 ◽  
Author(s):  
D. Roux ◽  
S. P. Singh
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Space Setting ◽  
Ky Fan

In this paper we prove a fixed point theorem for inward mappings uing a well-known result of Ky Fan type in Hilbert space setting.

Fixed Point Theorems for Compatible Mappings of Type (R) in 2-Metric Spaces

2015 ◽  
Vol 2 ◽  
pp. 17-27
Author(s):  
Oinam Budhichandra Singh ◽  
Th. Indubala ◽  
N. Leenthoi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Compatible Mappings

The aim of this paper is to introduce the concept of compatible mappings of type (R) in 2-metric spaces and to prove a coincidence point theorem and a fixed point theorem for compatible mappings of type (R) in 2-matric spaces.

scholarly journals Some fixed point theorems for nonconvex spaces

1998 ◽  
Vol 21 (1) ◽  
pp. 133-137 ◽  
Author(s):  
F. Jafari ◽  
V. M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Ky Fan

We give a theorem for nonconvex topological vector spaces which yields the classical fixed point theorems of Ky Fan, Kim, Kaczynski, Kelly and Namioka as immediate consequences, and prove a new fixed point theorem for set-valued maps on arbitrary topological vector spaces.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document