Rational Type Inequality with Applications to Voltera–Hammerstein Nonlinear Integral Equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhammad Sarwar ◽  
Mian Bahadur Zada ◽  
Stojan Radenović
Keyword(s):  
Integral Equations ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type Inequality ◽  
Nonlinear Integral Equations ◽  
Linear Integral ◽  
Complex Valued ◽  
Rational Type ◽  
Linear Integral Equations

AbstractThe aim of this work is to establish fixed point theorems under rational type contractions in the framework of complex-valued metric spaces. These theorems extend and generalize some prominent results in the present literature. Furthermore, as an application the existence result is given for the system of Volterra–Hammerstein non-linear integral equations.

Fixed points of set-valued F-contractions and its application to non-linear integral equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3377-3390 ◽  
Author(s):  
Satish Shukla ◽  
Dhananjay Gopal ◽  
Juan Martínez-Moreno
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Complete Metric Spaces ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued ?-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear integral equations.

scholarly journals Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdullah Shoaib ◽  
Qasim Mahmood ◽  
Aqeel Shahzad ◽  
Mohd Salmi Md Noorani ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Rational Contraction ◽  
Rational Type

AbstractThe objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued mapping in these spaces. A suitable example confirms our results. We also present an application for a generalized class of nonlinear integral equations. Our results generalize and extend the results of Karapınar et al. (IEEE Access 7:89026–89032, 2019).

scholarly journals Common Fixed Point Results for Six Mappings via Integral Contractions with Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Mian Bahadur Zada ◽  
Muhammad Sarwar ◽  
Nayyar Mehmood
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type Inequality ◽  
Dynamical Programming ◽  
System Of Functional Equations ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Common fixed point theorems for six self-mappings under integral type inequality satisfying (E.A) and (CLR) properties in the context of complex valued metric space (not necessarily complete) are established. The derived results are new even for ordinary metric spaces. We prove existence result for optimal unique solution of the system of functional equations used in dynamical programming with complex domain.

The Thermodynamic Bethe Ansatz and a Connection with Painlevé Equations

1997 ◽  
Vol 11 (01n02) ◽  
pp. 69-74
Author(s):  
Craig A. Tracy ◽  
Harold Widom
Keyword(s):  
Integral Equations ◽  
Bethe Ansatz ◽  
Painlevé Equations ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Painleve Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We summarize some recent connections between a class of nonlinear integral equations related to the thermodynamic Bethe Ansatz and a class of linear integral equations related to the Painlevé equations.

scholarly journals Linearization method for solving nonlinear integral equations

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
P. Darania ◽  
A. Ebadian ◽  
A. V. Oskoi
Keyword(s):  
Integral Equations ◽  
Piecewise Linear ◽  
Linearization Method ◽  
Nonlinear Integral Equations ◽  
Numerical Examples ◽  
Linear Integral ◽  
Linear Integral Equations ◽  
Methods Numerical

The objective of this paper is to assess both the applicability and the accuracy of linearization method in several problems of general nonlinear integral equations. This method provides piecewise linear integral equations which can be easily integrated. It is shown that the accuracy of linearization method can be substantially improved by employing variable steps which adjust themselves to the solution. This approach can reveal that, under this method, the nonlinear integral equations can be transformed into the linear integral equations which may be integrated using classical methods. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

scholarly journals Fixed-Point Theorems for α-Admissible Mappings with w-Distance and Applications to Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Fengrong Zhang ◽  
Haoyue Wang ◽  
Shuangqi Wu ◽  
Liangshi Zhao
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Nonlinear Integral Equations ◽  
Complete Metric Spaces

Two fixed-point theorems for α-admissible mappings satisfying contractive inequality of integral type with w-distance in complete metric spaces are proved. Our results extend and improve a few existing results in the literature. As applications, we use the fixed-point theorems obtained in this paper to establish solvability of nonlinear integral equations. Examples are included.

scholarly journals Existence of a common solution for a system of nonlinear integral equations via fixed point methods in b-metric spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 128-145 ◽  
Author(s):  
Oratai Yamaod ◽  
Wutiphol Sintunavarat ◽  
Yeol Je Cho
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Common Solution ◽  
Fixed Point Methods ◽  
Common Fixed Point Theorems

AbstractIn this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.

scholarly journals Generalized contraction mappings of rational type and applications to nonlinear integral equations

2018 ◽  
Vol 38 (1) ◽  
pp. 131-149
Author(s):  
José R. Morales ◽  
Edixon M. Rojas ◽  
Ravindra K. Bisht
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Generalized Contraction ◽  
Nonlinear Integral Equations ◽  
Contraction Mappings ◽  
New Class ◽  
Common Fixed Point Theorems ◽  
Rational Type

The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

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