scholarly journals Existence of local fractional integral equation via a measure of non-compactness with monotone property on Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Rabha W. Ibrahim ◽  
Ravi P. Agarwal ◽  
N. H. Can
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Partially Ordered ◽  
Fractional Integral Equation ◽  
Local Fractional Integral ◽  
Ordered Banach Spaces

AbstractIn this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone $\mathbb{K}$ K is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application to the existence of a local fractional integral equation.

scholarly journals Random Fixed Point Theorems of Random Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jiandong Yin ◽  
Zhongdong Liu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Monotone Operators ◽  
Hammerstein Integral Equation ◽  
Random Fixed Point ◽  
Partially Ordered ◽  
Ordered Banach Spaces

We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.

scholarly journals Fixed Point Theorems of Binary Contraction Comparable Operators and an Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Zhan Liu ◽  
Chuanxi Zhu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Large Class ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Nonlinear Problems ◽  
Existence Of Solution ◽  
Partially Ordered ◽  
Ordered Banach Spaces

The aim of this paper is to present the concept of binary comparable operators in partially ordered Banach spaces and prove several fixed point theorems under some contractive conditions. The results of this paper can be used to investigate a large class of nonlinear problems. As an application, we study the existence of solution of a nonlinear integral equation.

scholarly journals Solvability of a Parametric Fractional-Order Integral Equation Using Advance Darbo G-Contraction Theorem

Foundations ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 286-303
Author(s):  
Vishal Nikam ◽  
Dhananjay Gopal ◽  
Rabha W. Ibrahim
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Numerical Solutions ◽  
Applied Mathematics ◽  
Fractional Integrals ◽  
Local Conditions ◽  
Contraction Theorem ◽  
Fractional Integral Equation

The existence of a parametric fractional integral equation and its numerical solution is a big challenge in the field of applied mathematics. For this purpose, we generalize a special type of fixed-point theorems. The intention of this work is to prove fixed-point theorems for the class of β−G, ψ−G contractible operators of Darbo type and demonstrate the usability of obtaining results for solvability of fractional integral equations satisfying some local conditions in Banach space. In this process, some recent results have been generalized. As an application, we establish a set of conditions for the existence of a class of fractional integrals taking the parametric Riemann–Liouville formula. Moreover, we introduce numerical solutions of the class by using the set of fixed points.

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

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