scholarly journals Fixed point theorems in Fréchet algebras and Fréchet spaces and applications to nonlinear integral equations

2017 ◽  
Vol 11 (2) ◽  
pp. 340-357 ◽  
Author(s):  
Szymon Dudek
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness

In this paper, we present two new fixed point theorems in Fr?chet algebras and Fr?chet spaces. Our fixed point results are expressed with the help of family of measures of noncompactness and generalizes Darbo theorem. As an application, we establish some existence results for various types of nonlinear integral equations.

scholarly journals Compactness Conditions in the Study of Functional, Differential, and Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Józef Banaś ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Functional Differential ◽  
Functional Integral Equations ◽  
Differential And Integral Equations

We discuss some existence results for various types of functional, differential, and integral equations which can be obtained with the help of argumentations based on compactness conditions. We restrict ourselves to some classical compactness conditions appearing in fixed point theorems due to Schauder, Krasnosel’skii-Burton, and Schaefer. We present also the technique associated with measures of noncompactness and we illustrate its applicability in proving the solvability of some functional integral equations. Apart from this, we discuss the application of the mentioned technique to the theory of ordinary differential equations in Banach spaces.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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.

scholarly journals Fixed Point Theorems for ${\mathscr{Z}}_{\vartheta}$ -Contraction and Applications to Nonlinear Integral Equations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 120023-120029
Author(s):  
Xiangling Li ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Ekrem Savas
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equations

scholarly journals Fixed point theorems for (α-ψ)-contractive type mappings in uniform spaces and applications

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2781-2794
Author(s):  
Le Hung ◽  
Kieu Chi ◽  
Tran An
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Uniqueness Problem ◽  
Uniform Spaces ◽  
Nonlinear Integral Equations ◽  
Contractive Mappings ◽  
Contractive Type

In this paper, we prove some fixed point theorems for generalized (?-?)-contractive mappings in uniform spaces and apply them to study the existences-uniqueness problem for a class of nonlinear integral equations with unbounded deviations. We also give some examples to show that our results are effective.

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.

Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Józef Banaś
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Differential And Integral Equations

AbstractThe aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.

scholarly journals The Existence and Uniquenes Solution of Nonlinear Integral Equations via Common Fixed Point Theorems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1179
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Yongjin Li ◽  
Zhaohui Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed-point theorems on complex partial metric space. The presented results generalize and expand some of the well-known results in the literature. We also explore some of the applications of our key results.

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