scholarly journals On solution of generalized proportional fractional integral via a new fixed point theorem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Anupam Das ◽  
Iyad Suwan ◽  
Bhuban Chandra Deuri ◽  
Thabet Abdeljawad
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Integral ◽  
Strong Support ◽  
Existence Of Solution

AbstractThe aim of this paper is the solvability of generalized proportional fractional(GPF) integral equation at Banach space $\mathbb{E}$ E . Herein, we have established a new fixed point theorem which is then applied to the GPF integral equation in order to establish the existence of solution on the Banach space. At last, we have illustrated a genuine example that verified our theorem and gave a strong support to prove it.

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

scholarly journals The Existence and Attractivity of Solutions of an Urysohn Integral Equation on an Unbounded Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Abdalla Darwish ◽  
Józef Banaś ◽  
Ebraheem O. Alzahrani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Measures Of Noncompactness ◽  
Unbounded Interval ◽  
Real Functions ◽  
Half Axis

We prove a result on the existence and uniform attractivity of solutions of an Urysohn integral equation. Our considerations are conducted in the Banach space consisting of real functions which are bounded and continuous on the nonnegative real half axis. The main tool used in investigations is the technique associated with the measures of noncompactness and a fixed point theorem of Darbo type. An example showing the utility of the obtained results is also included.

Random fixed point theorem in generalized Banach space and applications

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Moulay Larbi Sinacer ◽  
Juan Jose Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
Existence Of Solution ◽  
Random Fixed Point ◽  
Random Differential Equations ◽  
Random Fixed Point Theorem

AbstractIn this paper, we prove some random fixed point theorems in generalized Banach spaces. We establish a random version of a Krasnoselskii-type fixed point theorem for the sum of a contraction random operator and a compact operator. The results are used to prove the existence of solution for random differential equations with initial and boundary conditions. Finally, some examples are given to illustrate the results.

scholarly journals Extension of Darbo’s fixed point theorem via shifting distance functions and its application

2022 ◽  
Vol 27 ◽  
pp. 1-14
Author(s):  
Hemant Kumar Nashine ◽  
Anupam Das
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Distance Function ◽  
Mixed Type ◽  
Fractional Integral ◽  
Infinite System ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Darbo’S Fixed Point Theorem

In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

scholarly journals On a fixed point theorem of Greguš

1986 ◽  
Vol 9 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Brian Fisher ◽  
Salvatore Sessa
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Convex Subset ◽  
Unique Common Fixed Point

We consider two selfmapsTandIof a closed convex subsetCof a Banach spaceXwhich are weakly commuting inX, i.e.‖TIx−ITx‖≤‖Ix−Tx‖   for   any   x   in   X,and satisfy the inequality‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖}for allx,yinC, where0<a<1. It is proved that ifIis linear and non-expansive inCand such thatICcontainsTC, thenTandIhave a unique common fixed point inC.

A new extension of Kannan’s fixed point theorem via F-contraction with application to integral equations

2021 ◽  
pp. 2250123
Author(s):  
Pradip Debnath
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Extended Version

Our aim is to introduce an updated and real generalization of Kannan’s fixed point theorem with the help of [Formula: see text]-contraction introduced by Wardowski for single-valued mappings. Our result can be useful to ascertain the existence of fixed point for a family of mappings for which neither the Wardowski’s result nor that of Kannan can be applied directly. Our result has been applied to solve a particular type of integral equation. Finally, we establish a Reich-type extended version of the main result.

scholarly journals An Application of Random Fixed Point Theorem in Integral Equation

2014 ◽  
Vol 9 (4) ◽  
pp. 57-61
Author(s):  
Mukti Gangopadhyay ◽  
◽  
Pritha Dan ◽  
M. Saha
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Random Fixed Point ◽  
Random Fixed Point Theorem
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