Fixed Point Theorems for Lipspchitzian Semigroups

1989 ◽  
Vol 32 (1) ◽  
pp. 90-97 ◽  
Author(s):  
Hajime ishihara

AbstractLet U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups

2017 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
AHMED H. SOLIMAN ◽  
MOHAMMAD IMDAD ◽  
MD AHMADULLAH

In this paper, we consider a new uniformly generalized Kannan type semigroup of self-mappings defined on a closed convex subset of a real Banach space equipped with uniform normal structure and employ the same to show that such semigroup of self-mappings admits a common fixed point provided the underlying semigroup of self-mappings has a bounded orbit.


2015 ◽  
Vol 97 (111) ◽  
pp. 239-251
Author(s):  
Seyit Temir

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K ? K be an I-asymptotically quasi-nonexpansive type mapping and I : K ? K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of T and I. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself I-asymptotically quasinonexpansive type mapping in Banach spaces. The results presented in this paper extend and generalize some recent work of Chang and Zhou [1], Wang [19], Yao and Wang [20] and many others.


2003 ◽  
Vol 16 (3) ◽  
pp. 243-248 ◽  
Author(s):  
B. C. Dhage ◽  
Donal O'Regan ◽  
Ravi P. Agarwal

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved.


2016 ◽  
Vol 24 (2) ◽  
pp. 27-43 ◽  
Author(s):  
Laszlo Balog ◽  
Vasile Berinde ◽  
Mădălina Păcurar

Abstract Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type. Our new results complement and extend recent related results [Berinde, V., Păcurar, M., The contraction principle for nonself mappings on Banach spaces endowed with a graph, J. Nonlinear Convex Anal. 16 (2015), no. 9, 1925-1936; Balog, L., Berinde, V., Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph, Carpathian J. Math. 32 (2016), no. 3 (in press)] and thus provide more general and flexible tools for studying nonlinear functional equations.


2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Nawab Hussain ◽  
Mohamed-Aziz Taoudi

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.


1995 ◽  
Vol 18 (4) ◽  
pp. 813-818
Author(s):  
Byung Soo Lee ◽  
Do Sang Kim ◽  
Gue Myung Lee ◽  
Sung Jin Cho

In this paper we defineg-nonexpansive andg-nonexpansive type fuzzy mappings and prove common fixed point theorems for sequences of fuzzy mappings satisfying certain conditions on a Banach space. Thus we obtain fixed point theorems for nonexpansive type multi-valued mappings.


1999 ◽  
Vol 4 (1) ◽  
pp. 49-59 ◽  
Author(s):  
G. Li ◽  
J. K. Kim

LetGbe a semitopological semigroup,Ca nonempty subset of a real Hilbert spaceH, andℑ={Tt:t∈G}a representation ofGas asymptotically nonexpansive type mappings ofCinto itself. LetL(x)={z∈H:infs∈Gsupt∈G‖Tts x−z‖=inft∈G‖Tt x−z‖}for eachx∈CandL(ℑ)=∩x∈C L(x). In this paper, we prove that∩s∈Gconv¯{Tts x:t∈G}∩L(ℑ)is nonempty for eachx∈Cif and only if there exists a unique nonexpansive retractionPofCintoL(ℑ)such thatPTs=Pfor alls∈GandP(x)∈conv¯{Ts x:s∈G}for everyx∈C. Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.


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