scholarly journals Existence of common fixed points via modified mann iteration in convex metric spaces and an invariant approximation result

2010 ◽  
Vol 41 (4) ◽  
pp. 335-348
Author(s):  
G.V.R. Babu ◽  
G.N. Alemayehu
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Space ◽  
Approximation Result ◽  
Mann Iteration ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Weakly Contractive

We prove the existence of common fixed points for two selfmaps $T$ and $f$ of a convex metric space $X$ via the convergence of modified Mann iteration where $T$ is a nonlinear $f$-weakly contractive selfmap of $X$ and range of $f$ is complete. An invariant approximation result is also proved.

Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces

2008 ◽  
Vol 15 (1) ◽  
pp. 39-43
Author(s):  
Ljubomir B. Ćirić ◽  
Nebojša T. Nikolić
Keyword(s):  
Metric Space ◽  
Convex Subset ◽  
Metric Spaces ◽  
Satisfy Condition ◽  
Convex Metric Space ◽  
Convex Metric Spaces ◽  
The Family

Abstract Let (𝑋, 𝑑) be a convex metric space, 𝐶 be a closed and convex subset of 𝑋 and let 𝐵(𝐶) be the family of all nonempty bounded subsets of 𝐶. In this paper some results are obtained on the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings 𝑆,𝑇 : 𝐶 → 𝐵(𝐶) which satisfy condition (2.1) below.

scholarly journals Common fixed points of multivalued F-contractions on metric spaces with a directed graph

2016 ◽  
Vol 32 (1) ◽  
pp. 1-12
Author(s):  
MUJAHID ABBAS ◽  
◽  
MONTHER R. ALFURAIDAN ◽  
TALAT NAZIR ◽  
◽  
...  
Keyword(s):  
Fixed Points ◽  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contraction Mappings

In this paper, we establish the existence of common fixed points of multivalued F-contraction mappings on a metric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature.

scholarly journals Approximating Common Fixed Points of an Evolution Family on a Metric Space via Mann Iteration

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Liang Luo ◽  
Rizwan Ullah ◽  
Gul Rahmat ◽  
Saad Ihsan Butt ◽  
Muhammad Numan
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Irrational Number ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Evolution Family ◽  
Mann Iteration ◽  
The Family ◽  
Families Of Operators ◽  
Mann Iteration Process

In this article, we present the set of all common fixed points of a subfamily of an evolution family in terms of intersection of all common fixed points of only two operators from the family; that is, for subset M of L , we have F M = F Y ϱ 1 , 0 ∩ F Y ϱ 2 , 0 , where ϱ 1 and ϱ 2 are positive and ϱ 1 / ϱ 2 is an irrational number. Furthermore, we approximate such common fixed points by using the modified Mann iteration process. In fact, we are generalizing the results from a semigroup of operators to evolution families of operators on a metric space.

scholarly journals Common fixed points of generalized almost nonexpansive mappings

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 11-18 ◽  
Author(s):  
Mujahid Abbas ◽  
Dejan Ilic
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Approximation Result ◽  
New Class ◽  
Invariant Approximation

The concept of a generalized almost nonexpansive mappings is introduced and the existence of common fixed points for this new class of mappings is proved. As an application, an invariant approximation result is obtained.

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