A distributed algorithm for computing a common fixed point of a family of strongly quasi-nonexpansive maps

2017 ◽  
Author(s):  
Ji Liu ◽  
Daniel Fullmer ◽  
Angelia Nedic ◽  
Tamer Basar ◽  
A. Stephen Morse
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distributed Algorithm ◽  
Nonexpansive Maps

scholarly journals A Distributed Algorithm for Computing a Common Fixed Point of a Family of Paracontractions

2016 ◽  
Vol 49 (18) ◽  
pp. 552-557 ◽  
Author(s):  
Daniel Fullmer ◽  
Lili Wang ◽  
A. Stephen Morse
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distributed Algorithm

scholarly journals Common Fixed Point of a Finite-step Iteration Algorithm Under Total Asymptotically Quasi-nonexpansive Maps

2019 ◽  
Vol 16 (3) ◽  
pp. 0654
Author(s):  
Abed Et al.
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Banach Space ◽  
Finite Family ◽  
Iteration Algorithm ◽  
Uniformly Convex ◽  
Nonexpansive Maps ◽  
Finite Step

      Throughout this paper, a generic iteration algorithm for a finite family of total asymptotically quasi-nonexpansive maps in uniformly convex Banach space is suggested. As well as weak / strong convergence theorems of this algorithm to a common fixed point are established. Finally, illustrative numerical example by using Matlab is presented.

scholarly journals Convergence Comparison of two Schemes for Common Fixed Points with an Application

2019 ◽  
Vol 32 (2) ◽  
pp. 81
Author(s):  
Salwa Salman Abed ◽  
Zahra Mahmood Mohamed Hasan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Nonexpansive Maps ◽  
Fredholm Functional

      Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

scholarly journals Some results on common fixed points and best approximation

2005 ◽  
Vol 36 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Abdul Rahim Khan ◽  
Abdul Latif ◽  
Arjamand Bano ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Best Approximation ◽  
Common Fixed Points ◽  
Fixed Point Result ◽  
Nonexpansive Maps

We prove a common fixed point result for $(f,g)$-nonexpansive maps and then derive certain results on best approximation. Our results generalize the results of Al-Thagafi [1], Jungck and Sessa [6], Khan, Hussain and Thaheem [8], Latif [9, 10] and Sahab, Khan and Sessa [12].

scholarly journals Common fixed points versus best approximations

2001 ◽  
Vol 32 (3) ◽  
pp. 181-186
Author(s):  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Best Approximation ◽  
Common Fixed Points ◽  
Normed Spaces ◽  
Best Approximations ◽  
Nonexpansive Maps ◽  
Common Fixed Point Theorem

We obtain a common fixed point theorem for $ (f,g) $-nonexpansive maps in $ p $-normed spaces. Some results on best approximation are also derived via common fixed points. Our results generalize and extend the work of Al-Thaghafi [J. Approx. Theory 85 (1996), 318-323], Khan and Khan [Approx. Theory & its Appl., 11 (1995), 1-5], Habiniak [J. Approx. Theory, 56 (1989), 241-244], Sahab, Khan and Sessa [J. Approx. Theory, 55 (1988), 349-351], and many of the others.

scholarly journals An abstract common fixed point principle and its applications

1996 ◽  
Vol 53 (1) ◽  
pp. 13-19
Author(s):  
Jacek R. Jachymski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Unit Interval ◽  
Nonexpansive Maps ◽  
Affine Maps ◽  
Fixed Point Principle ◽  
Kakutani Theorem ◽  
Commutative Family ◽  
Common Fixed Point Theorem

We establish a common fixed point principle for a commutative family of self-maps on an abstract set. This principle easily yields the Markoff-Kakutani theorem for affine maps, Kirk's theorem for nonexpansive maps and Cano's theorem for maps on the unit interval. As another application we obtain a new common fixed point theorem for a commutative family of maps on an arbitrary interval, which generalises an earlier result of Mitchell.

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