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.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

scholarly journals Some fixed point theorems on equivalent metric spaces

2021 ◽  
Vol 38 (1) ◽  
pp. 139-148
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
MARIANA CUFOIAN ◽  
ADRIANA MITRE
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Complete Metric Spaces

This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.

scholarly journals Common fixed point theorems without continuity and compatible property of maps

2017 ◽  
Vol 35 (3) ◽  
pp. 67-77 ◽  
Author(s):  
Vinod Bhardwaj ◽  
Vishal Gupta ◽  
Naveen Mani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Contraction Of Integral Type ◽  
Common Fixed Point Theorems

In this paper, without assuming continuity, commutativity and compatibility of self maps, some common fixed theorem for weak contraction of integral type in complete metric spaces are proved. An example and some remarks are also given to justify that our contraction is new and weaker than other existing contractions.

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 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 Integral type fixed point theorems for α-admissible mappings satisfying α-Ψ-Φ-contractive inequality

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3227-3234
Author(s):  
Ziad Badehian ◽  
Mohammad Asgari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Complete Metric Spaces

In this paper, we establishe some new fixed point theorems by ?-admissible mappings satisfying ?-?-?-contractive inequality of integral in complete metric spaces. Presented results can be considered as an extension of the theorems of Banach-Cacciopoli and Branciari.

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.

Fixed points of set-valued F-contractions and its application to non-linear integral equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3377-3390 ◽  
Author(s):  
Satish Shukla ◽  
Dhananjay Gopal ◽  
Juan Martínez-Moreno
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Complete Metric Spaces ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued ?-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear 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.

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