The extension of fixed point theorems for set valued mapping

2003 ◽  
Vol 13 (1-2) ◽  
pp. 277-286 ◽  
Author(s):  
Yimin Shi ◽  
Limei Ren ◽  
Xuyan Wang
2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
M. Djedidi ◽  
K. Nachi

We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.


2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hans-Peter A. Künzi ◽  
Olivier Olela Otafudu

In a previous work, we started investigating the concept of hyperconvexity in quasipseudometric spaces which we calledq-hyperconvexity or Isbell-convexity. In this paper, we continue our studies of this concept, generalizing further known results about hyperconvexity from the metric setting to our theory. In particular, in the present paper, we consider subspaces ofq-hyperconvex spaces and also present some fixed point theorems for nonexpansive self-maps on a boundedq-hyperconvex quasipseudometric space. In analogy with a metric result, we show among other things that a set-valued mappingT∗on aq-hyperconvexT0-quasimetric space (X, d) which takes values in the space of nonempty externallyq-hyperconvex subsets of (X, d) always has a single-valued selectionTwhich satisfiesd(T(x),T(y))≤dH(T∗(x),T∗(y))wheneverx,y∈X. (Here,dHdenotes the usual (extended) Hausdorff quasipseudometric determined bydon the set𝒫0(X)of nonempty subsets ofX.)


1988 ◽  
Vol 11 (2) ◽  
pp. 289-296 ◽  
Author(s):  
M. Imdad ◽  
M. S. Khan ◽  
S. Sessa

We generalize common fixed point theorems of Fisher and Sessa in complete metric spaces, using some conditions of weak commutativity between a set-valued mapping and a single-valued mapping. Suitable examples prove that these conditions do not imply each of the others.


2021 ◽  
Vol 20 ◽  
pp. 50-55
Author(s):  
Maha Mousa ◽  
Salwa Salman Abed

In this paper, inspired by the concept of metric space, two fixed point theorems for α−set-valued mapping T:₳ → CB(₳), h θ (Tp,Tq) ≤ α(dθ(p,q)) dθ(p,q), where α: (0,∞) → (0, 1] such that α(r) < 1, ∀ t ∈ [0,∞) ) are given in complete θ −metric and then extended for two mappings with R-weakly commuting property to obtain a common coincidence point.


Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.


2017 ◽  
Vol 5 (10) ◽  
pp. 140-143
Author(s):  
P.L. Powar ◽  
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◽  
G.R.K. Sahu ◽  
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