Fixed Point Theorems for Lipspchitzian Semigroups

1989 ◽  
Vol 32 (1) ◽  
pp. 90-97 ◽  
Author(s):  
Hajime ishihara
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Closed Subset ◽  
Fixed Point Theorems ◽  
Nonempty Subset ◽  
Continuous Representation ◽  
Semitopological Semigroup ◽  
Lipschitzian Mappings

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

Fixed point theorems for uniformly generalized Kannan type semigroup of self-mappings

2017 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
AHMED H. SOLIMAN ◽  
MOHAMMAD IMDAD ◽  
MD AHMADULLAH
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Real Banach Space ◽  
Normal Structure ◽  
Uniform Normal Structure

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.

scholarly journals Convergence theorems of a scheme for I-asymptotically quasi-nonexpansive type mapping in Banach space

2015 ◽  
Vol 97 (111) ◽  
pp. 239-251
Author(s):  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Recent Work ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Convergence Theorems ◽  
Type Mapping ◽  
Necessary And Sufficient

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.

scholarly journals Common fixed point theorems for a pair of countably condensing mappings in ordered banach spaces

2003 ◽  
Vol 16 (3) ◽  
pp. 243-248 ◽  
Author(s):  
B. C. Dhage ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Ordered Banach Space ◽  
Isotone Mappings ◽  
Common Fixed Point Theorems ◽  
Ordered Banach Spaces

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

scholarly journals Approximating Fixed Points of Nonself Contractive Type Mappings in Banach Spaces Endowed with a Graph

2016 ◽  
Vol 24 (2) ◽  
pp. 27-43 ◽  
Author(s):  
Laszlo Balog ◽  
Vasile Berinde ◽  
Mădălina Păcurar
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Closed Subset ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Contraction Principle ◽  
Nonlinear Functional ◽  
Contractive Type

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.

scholarly journals Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Nawab Hussain ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Ordered Banach Space ◽  
Nonlinear Integral Equations ◽  
Common Fixed Point Theorems ◽  
Ordered Banach Spaces ◽  
Nonlinear Mappings

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.

scholarly journals Common fixed points for nonexpansive type fuzzy mappings

1995 ◽  
Vol 18 (4) ◽  
pp. 813-818
Author(s):  
Byung Soo Lee ◽  
Do Sang Kim ◽  
Gue Myung Lee ◽  
Sung Jin Cho
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Common Fixed Point Theorems

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.

scholarly journals Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity

1999 ◽  
Vol 4 (1) ◽  
pp. 49-59 ◽  
Author(s):  
G. Li ◽  
J. K. Kim
Keyword(s):  
Hilbert Space ◽  
Convergence Theorem ◽  
Nonempty Subset ◽  
Real Hilbert Space ◽  
Ergodic Theorems ◽  
Semitopological Semigroup ◽  
Lipschitzian Mappings ◽  
Asymptotically Nonexpansive

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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