Fixed point theorem of nonexpansive mappings in convex metric spaces

1989 ◽  
Vol 10 (2) ◽  
pp. 183-188 ◽  
Author(s):  
Li Bing-you
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Convex Metric Spaces

scholarly journals Existence and approximation of fixed points in convex metric spaces

2014 ◽  
Vol 30 (2) ◽  
pp. 175-185
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
Generalized Nonexpansive Mapping ◽  
The Fixed Point Theorem

A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503–509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel’skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and CAT(0) spaces.

scholarly journals An extension of Assad-Kirk’s fixed point theorem for multivalued nonself mappings

2016 ◽  
Vol 32 (2) ◽  
pp. 147-155
Author(s):  
ISHAK ALTUN ◽  
◽  
GULHAN MINAK ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Convex Metric Spaces ◽  
Recent Developments

In the present paper, taking into account the recent developments on the theory of fixed point, we give some fixed point results for multivalued nonself mappings on complete metrically convex metric spaces. Our main result properly includes the famous Assad-Kirk fixed point theorem for nonself mappings. Also, we provide a nontrivial example which shows the motivation for such investigations of multivalued nonself contraction mappings.

scholarly journals Common fixed points for generalized asymptotically nonexpansive mappings

2012 ◽  
Vol 44 (1) ◽  
pp. 23-29
Author(s):  
Sumit Chandok ◽  
T. D. Narang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Asymptotically Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
The Subject ◽  
Common Fixed Point Theorem

A common fixed point theorem for noncommuting generalized asymptotically nonexpansive mappings has been obtained in convex metric spaces. As an application, a result on the set of best approximation is also derived for such class of mappings. The proved results unify and extend some of the known results on the subject.

scholarly journals Contractive definitions and discontinuity at fixed point

2017 ◽  
Vol 18 (1) ◽  
pp. 173 ◽  
Author(s):  
Ravindra K Bisht ◽  
R. P. Pant
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings

In this paper, we investigate some contractive definitions which are strong enough to generate a fixed point that do not force the mapping to be continuous at the fixed point. Finally, we obtain a fixed point theorem for generalized nonexpansive mappings in metric spaces by employing Meir-Keeler type conditions.<p style="-qt-paragraph-type: empty; -qt-block-indent: 0; text-indent: 0px; margin: 0px;"> </p>

Goebel and Kirk fixed point theorem for multivalued asymptotically nonexpansive mappings

2017 ◽  
Vol 33 (3) ◽  
pp. 335-342
Author(s):  
M. A. KHAMSI ◽  
◽  
A. R. KHAN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mapping ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Mann Iteration ◽  
Asymptotically Nonexpansive ◽  
Mann Iteration Process

We introduce the concept of a multivalued asymptotically nonexpansive mapping and establish Goebel and Kirk fixed point theorem for these mappings in uniformly hyperbolic metric spaces. We also define a modified Mann iteration process for this class of mappings and obtain an extension of some well-known results for singlevalued mappings defined on linear as well as nonlinear domains.

scholarly journals On coincidence theorems for a family of mappings in convex metric spaces

1987 ◽  
Vol 10 (3) ◽  
pp. 453-460
Author(s):  
Olga Hadzic
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Spaces ◽  
Coincidence Theorems ◽  
Common Fixed Point Theorem

In this paper, a theorem on common fixed points for a family of mappings defined on convex metric spaces is presented. This theorem is a generalization of the well known fixed point theorem proved by Assad and Kirk. As an application a common fixed point theorem in metric spaces with a convex structure is obtained.

scholarly journals Some new fixed point theorems for contractive and nonexpansive mappings

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 313-317 ◽  
Author(s):  
Rajendra Pant
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Vector Spaces ◽  
Ultrametric Spaces ◽  
Nonlinear Anal ◽  
New Type

In the present paper, we obtain some new fixed point theorems for set-valued contractive and nonexpansive mappings in the setting of ultrametric spaces. Our theorems complement, generalize and extend some well known results of Petalas and Vidalis [A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc 118(1993), 819-821.], Suzuki [A new type of fixed point theorem in metric spaces, Nonlinear Anal. 71(2009), 5313-5317.] and others.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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