BEST PROXIMITY POINT THEOREMS FOR CYCLIC QUASI-CONTRACTION MAPS IN UNIFORMLY CONVEX BANACH SPACES

2016 ◽  
Vol 95 (1) ◽  
pp. 149-156 ◽  
Author(s):  
NGUYEN VAN DUNG ◽  
VO THI LE HANG
Keyword(s):  
Banach Spaces ◽  
Point Theorem ◽  
Best Proximity Point ◽  
Negative Answer ◽  
Uniformly Convex ◽  
Contraction Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Contraction Maps

In this paper we first give a negative answer to a question of Amini-Harandi [‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim.56 (2013), 1667–1674] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi for cyclic strongly quasi-contractions are true under weaker assumptions.

scholarly journals Existence and Convergence Theorems of Best Proximity Points

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Banach Spaces ◽  
Convergence Theorem ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Best Proximity Points ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Relatively Nonexpansive

The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.

scholarly journals Fixed point approximation of Presic nonexpansive mappings in product of CAT (0) spaces

2016 ◽  
Vol 32 (3) ◽  
pp. 315-322
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
VASILE BERINDE ◽  
ABDUL RAHIM KHAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Control Parameters ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

We obtain a fixed point theorem for Presiˇ c nonexpansive mappings on the product of ´ CAT (0) spaces and approximate this fixed points through Ishikawa type iterative algorithms under relaxed conditions on the control parameters. Our results are new in the literature and are valid in uniformly convex Banach spaces.

scholarly journals Cyclic pairs and common best proximity points in uniformly convex Banach spaces

2017 ◽  
Vol 15 (1) ◽  
pp. 711-723
Author(s):  
Moosa Gabeleh ◽  
P. Julia Mary ◽  
A.Anthony Eldred Eldred ◽  
Olivier Olela Otafudu
Keyword(s):  
Fixed Point ◽  
Nonlinear Programming ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Best Proximity Point ◽  
Nonlinear Programming Problem ◽  
Uniformly Convex ◽  
Common Best Proximity Point ◽  
Uniformly Convex Banach Spaces ◽  
Strictly Convex Banach Spaces

Abstract In this article, we survey the existence, uniqueness and convergence of a common best proximity point for a cyclic pair of mappings, which is equivalent to study of a solution for a nonlinear programming problem in the setting of uniformly convex Banach spaces. Finally, we provide an extension of Edelstein’s fixed point theorem in strictly convex Banach spaces. Examples are given to illustrate our main conclusions.

scholarly journals Optimal Approximate Solutions of Fixed Point Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
S. Sadiq Basha ◽  
N. Shahzad ◽  
R. Jeyaraj
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Approximate Solutions ◽  
Uniformly Convex ◽  
Optimal Approximate Solution ◽  
Uniformly Convex Banach Spaces

The main objective of this paper is to present some best proximity point theorems for K-cyclic mappings and C-cyclic mappings in the frameworks of metric spaces and uniformly convex Banach spaces, thereby furnishing an optimal approximate solution to the equations of the form where is a non-self mapping.

scholarly journals A note on best approximation and invertibility of operators on uniformly convex Banach spaces

1991 ◽  
Vol 14 (3) ◽  
pp. 611-614 ◽  
Author(s):  
James R. Holub
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Best Approximation ◽  
Bounded Linear Operator ◽  
Convex Banach Space ◽  
Sufficient Condition ◽  
Uniformly Convex ◽  
Bounded Linear ◽  
Uniformly Convex Banach Spaces

It is shown that ifXis a uniformly convex Banach space andSa bounded linear operator onXfor which‖I−S‖=1, thenSis invertible if and only if‖I−12S‖<1. From this it follows that ifSis invertible onXthen either (i)dist(I,[S])<1, or (ii)0is the unique best approximation toIfrom[S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.

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