scholarly journals Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

2022 ◽  
Vol 27 (1) ◽  
pp. 91-101
Author(s):  
Prabavathy Magadevan ◽  
Saravanan Karpagam ◽  
Erdal Karapınar
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Best Proximity Point ◽  
Auxiliary Function ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Related Literature ◽  
Contraction Map ◽  
Nonempty Convex ◽  
The Given

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

scholarly journals A Study on p-Cyclic Orbital Geraghty type Contractions

2018 ◽  
Vol 7 (4.10) ◽  
pp. 883 ◽  
Author(s):  
M. L.Suresh ◽  
T. Gunasekar ◽  
S. Karpagam ◽  
B. Zlatanov ◽  
. .
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Periodic Point ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Best Proximity Point ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Space Setting

Consider a metric space  and the non empty sub sets, of X. A map called p-cyclic orbital Geraghty type of contraction is introduced.  Convergence of a unique fixed point and a best proximity point for this map is obtained in a uniformly convex Banach space setting.  Also, this best proximity point is the unique periodic point of such a map.  

A Generalization of a Fixed Point Theorem of Goebel, Kirk and Shimi

1976 ◽  
Vol 19 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Joseph Bogin
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Compact Convex ◽  
Continuous Mapping ◽  
Normal Structure ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Weakly Compact ◽  
Image Position

In [7], Goebel, Kirk and Shimi proved the following:Theorem. Let X be a uniformly convex Banach space, K a nonempty bounded closed and convex subset of X, and F:K→K a continuous mapping satisfying for each x, y∈K:(1)where ai≥0 and Then F has a fixed point in K.In this paper we shall prove that this theorem remains true in any Banach space X, provided that K is a nonempty, weakly compact convex subset of X and has normal structure (see Definition 1 below).

scholarly journals Fixed points of mappings satisfying semicontractivity conditions

1992 ◽  
Vol 53 (1) ◽  
pp. 25-38
Author(s):  
Jürgen Schu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Opial’S Condition ◽  
Asymptotically Nonexpansive

AbstractLet A be a subset of a Banach space E. A mapping T: A →A is called asymptoically semicontractive if there exists a mapping S: A×A→A and a sequence (kn) in [1, ∞] such that Tx=S(x, x) for all x ∈A while for each fixed x ∈A, S(., x) is asymptotically nonexpansive with sequence (kn) and S(x,.) is strongly compact. Among other things, it is proved that each asymptotically semicontractive self-mpping T of a closed bounded and convex subset A of a uniformly convex Banach space E which satisfies Opial's condition has a fixed point in A, provided s has a certain asymptoticregurity property.

scholarly journals Weak and strong convergence to fixed points of asymptotically nonexpansive mappings

1991 ◽  
Vol 43 (1) ◽  
pp. 153-159 ◽  
Author(s):  
J. Schu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Fourth Kind

Let T be an asymptotically nonexpansive self-mapping of a closed bounded and convex subset of a uniformly convex Banach space which satisfies Opial's condition. It is shown that, under certain assumptions, the sequence given by xn+1 = αnTn(xn) + (1 - αn)xn converges weakly to some fixed point of T. In arbitrary uniformly convex Banach spaces similar results are obtained concerning the strong convergence of (xn) to a fixed point of T, provided T possesses a compact iterate or satisfies a Frum-Ketkov condition of the fourth kind.

scholarly journals Approximating fixed points by ishikawa iterates

1989 ◽  
Vol 40 (1) ◽  
pp. 113-117 ◽  
Author(s):  
M. Maiti ◽  
M.K. Ghosh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex

In a uniformly convex Banach space the convergence of Ishikawa iterates to a fixed point is discussed for nonexpansive and generalised nonexpansive mappings.

Asymptotic centres of filters on uniformly rotund spaces

1976 ◽  
Vol 15 (1) ◽  
pp. 87-96
Author(s):  
John Staples
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Convex Banach Space ◽  
Bounded Sequence ◽  
Uniform Convexity ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Filter Base

The notion of asymptotic centre of a bounded sequence of points in a uniformly convex Banach space was introduced by Edelstein in order to prove, in a quasi-constructive way, fixed point theorems for nonexpansive and similar maps.Similar theorems have also been proved by, for example, adding a compactness hypothesis to the restrictions on the domain of the maps. In such proofs, which are generally less constructive, it may be possible to weaken the uniform convexity hypothesis.In this paper Edelstein's technique is extended by defining a notion of asymptotic centre for an arbitrary set of nonempty bounded subsets of a metric space. It is shown that when the metric space is uniformly rotund and complete, and when the set of bounded subsets is a filter base, this filter base has a unique asymptotic centre. This fact is used to derive, in a uniform way, several fixed point theorems for nonexpansive and similar maps, both single-valued and many-valued.Though related to known results, each of the fixed point theorems proved is either stronger than the corresponding known result, or has a compactness hypothesis replaced by the assumption of uniform convexity.

scholarly journals Monotone asymptotic pointwise contractions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3291-3294 ◽  
Author(s):  
Dehaish Bin ◽  
Mohamed Khamsi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Monotone Mappings ◽  
Uniformly Convex ◽  
Convex Metric Space ◽  
Uniformly Convex Metric Space

In this work, we extend the fixed point result of Kirk and Xu for asymptotic pointwise nonexpansive mappings in a uniformly convex Banach space to monotone mappings defined in a hyperbolic uniformly convex metric space endowed with a partial order.

scholarly journals Best proximity point theorems for weak cyclic Kannan contractions

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 145-154 ◽  
Author(s):  
Ancuţa Petric
Keyword(s):  
Banach Space ◽  
Best Proximity Point ◽  
Convex Banach Space ◽  
Existence Results ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Best Proximity Points ◽  
Kannan Contraction

In this paper we introduce the notion of weak cyclic Kannan contraction. We give some convergence and existence results for best proximity points for weak cyclic Kannan contractions in the setting of a uniformly convex Banach space.

scholarly journals Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

2005 ◽  
Vol 2005 (11) ◽  
pp. 1685-1692 ◽  
Author(s):  
Somyot Plubtieng ◽  
Rabian Wangkeeree
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Completely Continuous

Suppose thatCis a nonempty closed convex subset of a real uniformly convex Banach spaceX. LetT:C→Cbe an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that ifTis uniformlyL-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point ofT.

scholarly journals Inertial Accelerated Algorithm for Fixed Point of Asymptotically Nonexpansive Mapping in Real Uniformly Convex Banach Spaces

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 147
Author(s):  
Murtala Haruna Harbau ◽  
Godwin Chidi Ugwunnadi ◽  
Lateef Olakunle Jolaoso ◽  
Ahmad Abdulwahab
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Banach Space ◽  
Asymptotically Nonexpansive Mapping ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Mann Algorithm

In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.

Sign in / Sign up

Export Citation Format

Share Document