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 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 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 Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1253-1264 ◽  
Author(s):  
Hüseyin Işik ◽  
Duran Türkoğlu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Nonlinear Problems ◽  
Monotone Mappings ◽  
Mixed Monotone Property

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

scholarly journals Existence of solution of Urysohn integral equation through generalized contractive mapping

2018 ◽  
Vol 38 (2) ◽  
pp. 101-113
Author(s):  
Om Prakash Chauhan ◽  
Deepak Singh ◽  
Vishal Joshi ◽  
Mahendra Singh Rathore
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Operator Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Partially Ordered ◽  
The Given ◽  
Complex Valued

In this note, we establish the existence of fixed point through fixed point theorems in the setting of partially ordered complex valued b- metric spaces. Then this fixed point is co-related as solution of  equivalent operator equation of the Urysohn integral equation. In this process to make our results more authentic and meaningful we adopt an innovative way through visualling the given example supporting our findings. Naturally our results generalize some existing results.

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

scholarly journals A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 15
Author(s):  
Maryam Ramezani ◽  
Hamid Baghani ◽  
Ozgur Ege ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Convex Sets ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Modular Space ◽  
Ordinate Axis ◽  
Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

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