scholarly journals Approximation of the Fixed Point for Unified Three-Step Iterative Algorithm with Convergence Analysis in Busemann Spaces

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 26
Author(s):  
Hassan Almusawa ◽  
Hasanen A. Hammad ◽  
Nisha Sharma
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Iterative Scheme ◽  
Uniformly Convex ◽  
Iterative Schemes ◽  
Convergence Results

In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δ-convergence results of mappings that satisfy the condition (Eμ) in the framework of uniformly convex Busemann space are obtained. Our results generalize several existing results in the same direction.

scholarly journals Convergence of Infinite Family of Multivalued Quasi-Nonexpansive Mappings Using Multistep Iterative Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Renu Chugh ◽  
Sanjay Kumar
Keyword(s):  
Real Banach Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Finite Family ◽  
Countable Family ◽  
Uniformly Convex ◽  
Iterative Schemes ◽  
Strong And Weak Convergence ◽  
Convergence Results

We prove strong and weak convergence results using multistep iterative sequences for countable family of multivalued quasi-nonexpansive mappings by using some conditions in uniformly convex real Banach space. The results presented extended and improved the corresponding result of Zhang et al. (2013), Bunyawat and Suantai (2012), and some others from finite family, one countable family, and two countable families tok-number of countable families of multivalued quasi-nonexpansive mappings. Also we used a numerical example in C++ computational programs to prove that the iterative scheme we used has better rate of convergence than other existing iterative schemes.

scholarly journals Algorithmic Approach to the Equilibrium Points and Fixed Points

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Lijin Guo ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Equilibrium Points ◽  
Fixed Point Problems ◽  
Algorithmic Approach

The equilibrium and fixed point problems are considered. An iterative algorithm is presented. Convergence analysis of the algorithm is provided.

scholarly journals Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Noureddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Common Fixed Points ◽  
Nonexpansive Semigroup ◽  
Iteration Algorithm ◽  
Uniformly Convex ◽  
Modular Spaces ◽  
Nonexpansive Semigroups ◽  
Convergence Results

Abstract In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.

scholarly journals $$\alpha $$-Firmly nonexpansive operators on metric spaces

2022 ◽  
Vol 24 (1) ◽  
Author(s):  
Arian Bërdëllima ◽  
Florian Lauster ◽  
D. Russell Luke
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Metric Spaces ◽  
Uniformly Convex ◽  
Point Mapping ◽  
Splitting Algorithms ◽  
Uniformly Convex Spaces ◽  
Cluster Points ◽  
Convex Spaces

AbstractWe extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

scholarly journals Approximating Fixed Points Using a Faster Iterative Method and Application to Split Feasibility Problems

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 90
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Arshad ◽  
Zhenhua Ma
Keyword(s):  
Iterative Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Iterative Schemes ◽  
Split Feasibility Problems ◽  
Mild Conditions ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
The Many ◽  
Split Feasibility

In this article, the recently introduced iterative scheme of Hassan et al. (Math. Probl. Eng. 2020) is re-analyzed with the connection of Reich–Suzuki type nonexpansive (RSTN) maps. Under mild conditions, some important weak and strong convergence results in the context of uniformly convex Banach spaces are provided. To support the main outcome of the paper, we provide a numerical example and show that this example properly exceeds the class of Suzuki type nonexpansive (STN) maps. It has been shown that the Hassan et al. iterative scheme of this example is more useful than the many other iterative schemes. We provide an application of our main results to solve split feasibility problems in the setting of RSTN maps. The presented outcome is new and compliments the corresponding results of the current literature.

scholarly journals Common Fixed Points for Weak and Strong Convergence Results

2016 ◽  
Vol 4 (2) ◽  
pp. 340
Author(s):  
S. C. Shrivastava
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Results

<div><p> <em>In this paper, we study the approximation of common fixed points for more general classes of mappings through weak and strong convergence results of an iterative scheme in a uniformly convex Banach space. Our results extend and improve some known recent results.</em></p></div>

AN ITERATIVE SCHEME FOR FIXED POINT PROBLEMS

2021 ◽  
Vol 10 (5) ◽  
pp. 2295-2316
Author(s):  
F. Akutsah ◽  
O. K. Narain ◽  
K. Afassinou ◽  
A. A. Mebawondu
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Satisfying Condition ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Examples ◽  
Convergence Results ◽  
The Stability

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex Banach space. In addition, with the aid of numerical examples, we established that our newly proposed iterative scheme is faster than the iterative process introduced by Ullah et al., [26], Karakaya et al., [16], Abass et. al. [1] and some existing iterative scheme in literature. More so, the stability of our newly proposed iterative process is presented and we also gave some numerical examples to display the efficiency of our proposed algorithm.

scholarly journals Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 522 ◽  
Author(s):  
Javid Ali ◽  
Faeem Ali ◽  
Puneet Kumar
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Numerical Example ◽  
Matlab Program ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki’s generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that the considered iterative scheme converges faster than some other known iterations for Suzuki’s generalized non-expansive mappings. To support our claim, we give an illustrative numerical example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

scholarly journals Approximation of Fixed Points for Suzuki's Generalized Non-Expansive Mappings

2019 ◽  
Author(s):  
Javid Ali ◽  
Faeem Ali ◽  
Puneet Kumar
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Matlab Program ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

scholarly journals Iterative Algorithm for Mappings Satisfying Bγ,μ Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Iterative Algorithm ◽  
Iterative Algorithms ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Example ◽  
Strong And Weak Convergence ◽  
Convergence Results

In this article, we introduce a novel iterative algorithm to approximate fixed point of mappings with Bγ,μ condition. We establish some strong and weak convergence results in a uniformly convex Banach space. Using a numerical example, we compare the speed of the proposed algorithm with some leading iterative algorithms.

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