scholarly journals Coupled fixed points and α-dense curves

2016 ◽  
Vol 32 (3) ◽  
pp. 323-330
Author(s):  
G. GARCIA ◽  
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonexpansive Mappings ◽  
Volterra Type ◽  
System Of Integral Equations ◽  
Compactness Condition ◽  
New Iterative Method ◽  
Coupled Fixed Points

We present a new iterative method, based on the so called α-dense curves, to approximate coupled fixed points of nonexpansive mappings. Compactness condition on the mapping or its domain of definition is necessary. As application, we construct a sequence which converges to a solution of certain system of integral equations of Volterra type.

scholarly journals Nonlinear Dynamics, Fixed Points and Coupled Fixed Points in Generalized Gauge Spaces with Applications to a System of Integral Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Adrian Petruşel ◽  
Gabriela Petruşel
Keyword(s):  
Nonlinear Dynamics ◽  
Fixed Points ◽  
Integral Equations ◽  
Successive Approximations ◽  
Discrete Dynamics ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Generalized Metric ◽  
Multivalued Operators ◽  
Coupled Fixed Points

We will discuss discrete dynamics generated by single-valued and multivalued operators in spaces endowed with a generalized metric structure. More precisely, the behavior of the sequence(fn(x))n∈Nof successive approximations in complete generalized gauge spaces is discussed. In the same setting, the case of multivalued operators is also considered. The coupled fixed points for mappingst1:X1×X2→X1andt2:X1×X2→X2are discussed and an application to a system of nonlinear integral equations is given.

scholarly journals Convergence of a General Composite Iterative Method for a Countable Family of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shuang Wang
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Countable Family

We propose a general composite iterative method for computing common fixed points of a countable family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and complement the corresponding ones announced by many others.

scholarly journals Coupled Optimal Results with an Application to Nonlinear Integral Equations

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 73
Author(s):  
Pulak Konar ◽  
Sumit Chandok ◽  
Shrutinil Dutta ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonlinear Integral Equation ◽  
Nonlinear Integral Equations ◽  
Control Functions ◽  
Coupled Fixed Points

In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.

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.

scholarly journals A novel iterative approach for solving common fixed point problems in Geodesic spaces with convergence analysis

2021 ◽  
Vol 37 (2) ◽  
pp. 145-160
Author(s):  
THANATPORN BANTAOJAI ◽  
CHANCHAL GARODIA ◽  
IZHAR UDDIN ◽  
NUTTAPOL PAKKARANANG ◽  
PANU YIMMUANG
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Convergence Analysis ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Iterative Approach ◽  
Mild Conditions ◽  
New Iterative Method

In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we provide some non-trivial examples to show efficiency and comparison with many previously existing methods.

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