scholarly journals Modified inertial double Mann type iterative algorithm for a bivariate weakly nonexpansive operator

2020 ◽  
Vol 36 (1) ◽  
pp. 127-139
Author(s):  
ANANTACHAI PADCHAROEN ◽  
KAMONRAT SOMBUT
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Iterative Algorithm ◽  
Convex Subset ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Nonexpansive Operator ◽  
The One

"We introduce a modified inertial double Mann type iterative method to approximate coupled solutions of a bivariate nonexpansive operator T : C x C→ C, where C is a nonempty closed and convex subset of a Hilbert space. The one theorem and complement important old and recent results in coupled fixed point theory. Some appropriate examples to illustrate our results and their generalization are also given. "

scholarly journals Coupled Coincidence Point Theorems for New Types of Mixed Monotone Multivalued Mappings in Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chalongchai Klanarong ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Recent Developments

We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are also given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings.

scholarly journals On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Mi Zhou ◽  
Xiao-Lan Liu ◽  
Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Common Property ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
Contraction Condition ◽  
New Type ◽  
The One

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

scholarly journals Convergence theorems for fixed point iterative methods defined as admissible perturbations of a nonlinear operator

2013 ◽  
Vol 29 (1) ◽  
pp. 9-18
Author(s):  
VASILE BERINDE ◽  
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonlinear Operator ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Of View ◽  
Iterative Approximation ◽  
Convergence Theorems ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general fixed point iterative method defined by means of the new concept of admissible perturbation of a nonlinear operator, introduced in [Rus, I. A., An abstract point of view on iterative approximation of fixed points, Fixed Point Theory 13 (2012), No. 1, 179–192]. The obtained convergence theorems extend and unify some fundamental results in the iterative approximation of fixed points due to Petryshyn [Petryshyn, W. V., Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl. 14 (1966), 276–284] and Browder and Petryshyn [Browder, F. E. and Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), No. 2, 197–228].

scholarly journals A new approach on coupled fixed point theory in JS-metric spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 323-336 ◽  
Author(s):  
Tanusri Senapati ◽  
◽  
Lakshmi Kanta Dey ◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
New Approach

scholarly journals Fixed point theory and complementarity problems in Hilbert space

1987 ◽  
Vol 36 (2) ◽  
pp. 295-310 ◽  
Author(s):  
G. Isac
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Fixed Point Theory ◽  
Point Theory

In this paper we study both the implicit and the explicit complementarity problem using some special and interesting connections between the complementarity problem and fixed point theory in Hilbert space.

scholarly journals Cyclic Iterative Method for Strictly Pseudononspreading in Hilbert Space

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Bin-Chao Deng ◽  
Tong Chen ◽  
Zhi-Fang Li
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Hilbert Space ◽  
Cyclic Algorithm ◽  
The Common

Let{Ti}i=1NbeNstrictly pseudononspreading mappings defined on closed convex subsetCof a real Hilbert spaceH. Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality〈(γf-μB)x*,v-x*〉≤0,∀v∈⋂i=1NFix(Ti).

scholarly journals Stability for a New Class of GNOVI with (γG,λ)-Weak-GRD Mappings in Positive Hilbert Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Hong Gang Li ◽  
Yongqin Yang ◽  
Mao Ming Jin ◽  
Qinghua Zhang
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Variational Inclusions ◽  
New Class ◽  
Set Up ◽  
The Stability

By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions) with(γG,λ)-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained.

scholarly journals On Berinde’s method for comparing iterative processes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Constantin Zălinescu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Iterative Processes ◽  
The One

AbstractIn the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl. 2:97–105, 2004) because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde. The aim of this note is to prove this almost obvious assertion and to discuss briefly several papers that cite the mentioned Berinde’s paper and use his method for comparing iterative processes.

scholarly journals Existence and uniqueness of the solutions of some classes of integral equations C*-algebra-valued b-metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 726-742
Author(s):  
Esad Jakupović ◽  
Hashem Masiha ◽  
Zoran Mitrović ◽  
Seyede Razavi ◽  
Reza Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Point Theory ◽  
C Algebra ◽  
Coupled Fixed Points

Introduction/purpose: The aim of the paper is to establish some coupled fixed point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. Methods: The method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. Results: New results were obtained on coupled fixed points in C*-algebra-valued b-metric space. Conclusion: The obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations.

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