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.

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 Related fixed point results for cyclic contractions on G-metric spaces and application

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 853-869 ◽  
Author(s):  
Hassen Aydi ◽  
Abdelbasset Felhi ◽  
Slah Sahmim
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Cyclic Contractions

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

scholarly journals Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Gui-Xiu Chen ◽  
Shamoona Jabeen ◽  
Saif Ur Rehman ◽  
Ahmed Mostafa Khalil ◽  
Fatima Abbas ◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Nonlinear Integral Equations ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Point Analysis ◽  
Cone Metric

AbstractIn this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

scholarly journals An Extended b -Metric-Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Nonlinear Integral Equations ◽  
Type Space ◽  
Contractive Mappings ◽  
Underlying Space

In this paper, the concept of sequential p -metric spaces has been introduced as a generalization of usual metric spaces, b -metric spaces and specially of p -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems.

scholarly journals Nonlinear generalized cyclic contractions in complete G-metric spaces and applications to integral equations

2013 ◽  
Vol 18 (2) ◽  
pp. 160-176 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Cyclic Contractions

In this paper we introduce generalized cyclic contractions in G-metric spaces and establish some fixed point theorems. The presented theorems extend and unify various known fixed point results. Examples are given in the support of these results. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is given.

scholarly journals Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 34 ◽  
Author(s):  
Hamid Faraji ◽  
Dragana Savić ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Nonlinear Integral Equations ◽  
Contractive Mappings ◽  
Contraction Type

In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral equations are also given.

scholarly journals Coupled fixed point theorems for contractive mappings involving new function classes and applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1893-1907 ◽  
Author(s):  
Arslan Ansari ◽  
Hüseyin Işik ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Ordered Metric Spaces ◽  
Contractive Mappings ◽  
Function Classes

The aim of this paper is to introduce the notions of ?-(F,H)-(?,?) and ?-(F,H)-(?,?) contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.

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