A Darbo fixed point theory approach towards the existence of a functional integral equation in a Banach algebra

2019 ◽  
Vol 358 ◽  
pp. 111-118 ◽  
Author(s):  
Mausumi Sen ◽  
Dipankar Saha ◽  
R.P. Agarwal
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Functional Integral ◽  
Theory Approach

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

scholarly journals Convergence Comparison of two Schemes for Common Fixed Points with an Application

2019 ◽  
Vol 32 (2) ◽  
pp. 81
Author(s):  
Salwa Salman Abed ◽  
Zahra Mahmood Mohamed Hasan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Nonexpansive Maps ◽  
Fredholm Functional

      Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

Sign in / Sign up

Export Citation Format

Share Document