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 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 (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.

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.

scholarly journals Generalized contraction mappings of rational type and applications to nonlinear integral equations

2018 ◽  
Vol 38 (1) ◽  
pp. 131-149
Author(s):  
José R. Morales ◽  
Edixon M. Rojas ◽  
Ravindra K. Bisht
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Generalized Contraction ◽  
Nonlinear Integral Equations ◽  
Contraction Mappings ◽  
New Class ◽  
Common Fixed Point Theorems ◽  
Rational Type

The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

scholarly journals Expansive Mappings and Their Applications in Modular Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
A. Azizi ◽  
R. Moradi ◽  
A. Razani
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Nonlinear Integral Equations ◽  
Modular Spaces

Some fixed point theorems forρ-expansive mappings in modular spaces are presented. As an application, two nonlinear integral equations are considered and the existence of their solutions is proved.

scholarly journals Sequential Extended S -Metric Spaces and Relevant Fixed Point Results with Application to Nonlinear Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Abdollah Karami ◽  
Shaban Sedghi ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonlinear Integral Equations

In this paper, the notion of sequential ς p -metric spaces has been introduced as a generalization of usual S -metric spaces, S b -metric spaces, S J S metric spaces, and specially of S p -metric spaces. In view of this notion, we prove some fixed point theorems for some classes of ς p -rational Geraghty JS-contractions over such spaces. A supporting example and an application have been given in order to examine the validity of the obtained results.

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