scholarly journals An Iterative Approximation Method for a Common Fixed Point of Two Pseudocontractive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Approximation Method ◽  
Finite Family ◽  
Convex Minimization Problem ◽  
Iterative Approximation ◽  
Pseudocontractive Mappings ◽  
The Common ◽  
Iterative Approximation Method ◽  
Fixed Point Sets

We introduce an iterative process for finding an element in the common fixed point sets of two continuous pseudocontractive mappings. As a consequence, we provide an approximation method for a common fixed point of a finite family of pseudocontractive mappings. Furthermore, our convergence theorem is applied to a convex minimization problem. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptoticallyk-Strict Pseudocontractive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Important Class ◽  
Convergence Theorems ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptoticallyk-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals Approximation Analysis for a Common Fixed Point of Finite Family of Mappings Which Are Asymptoticallyk-Strict Pseudocontractive in the Intermediate Sense

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Convex Sets ◽  
Common Fixed Points ◽  
Finite Family ◽  
Important Class ◽  
Pseudocontractive Mappings ◽  
Approximation Analysis ◽  
Uniformly Continuous

We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous asymptoticallyki-strict pseudocontractive mappings in the intermediate sense fori=1,2,…,N. The projection ofx0onto the intersection of closed convex setsCnandQnfor eachn≥1is not required. Moreover, the restriction that the interior of common fixed points is nonempty is not required. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
O. A. Daman ◽  
H. Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iteration Method ◽  
Finite Family ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Pseudocontractive Mappings ◽  
Nonlinear Mappings

It is our purpose, in this paper, to prove strong convergence of Halpern-Ishikawa iteration method to a common fixed point of finite family of Lipschitz pseudocontractive mappings. There is no compactness assumption imposed either onCor onT. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.

scholarly journals A New Approximation Method for Common Fixed Points of a Finite Family of Generalized Asymptotically Quasinonexpansive Mappings in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Pornsak Yatakoat ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Approximation Method ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Finite Family ◽  
Strong And Weak Convergence

We introduce a new iterative scheme to approximate a common fixed point for a finite family of generalized asymptotically quasinonexpansive mappings. Several strong and weak convergence theorems of the proposed iteration in Banach spaces are established. The main results obtianed in this paper generalize and refine many known results in the current literature.

scholarly journals Common fixed point theorem on Proinov type mappings via simulation function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Badr Alqahtani ◽  
Sara Salem Alzaid ◽  
Andreea Fulga ◽  
Seher Sultan Yeşilkaya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Simulation Function ◽  
Type Mapping ◽  
The Common ◽  
Common Fixed Point Theorem

AbstractIn this paper, we aim to discuss the common fixed point of Proinov type mapping via simulation function. The presented results not only generalize, but also unify the corresponding results in this direction. We also consider an example to indicate the validity of the obtained results.

scholarly journals Fixed point and a Cantilever beam problem in a partial b-metric space

2021 ◽  
Vol 13 (2) ◽  
pp. 506-518
Author(s):  
Anita Tomar ◽  
Meena Joshi ◽  
Venkatesh Bhatt
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Cantilever Beam ◽  
Metric Space ◽  
Elastic Beam ◽  
The Common ◽  
Type Contraction

Abstract We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

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