scholarly journals Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays

2015 ◽  
Author(s):  
Poom Kumam ◽  
Parin Chaipunya
Keyword(s):  
Fixed Point ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Cyclic Operators

Fixed point theorems for Zamfirescu mappings in metric spaces endowed with a graph

2015 ◽  
Vol 31 (3) ◽  
pp. 297-305
Author(s):  
FLORIN BOJOR ◽  
◽  
MAGNOLIA TILCA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cyclic Operators

Let (X, d) be a metric space endowed with a graph G such that the set V (G) of vertices of G coincides with X. We define the notion of G-Zamfirescu maps and obtain a fixed point theorem for such mappings. This extends and subsumes many recent results which were obtained for mappings on metric spaces endowed with a graph and for cyclic operators.

scholarly journals A Solution for Volterra Fractional Integral Equations by Hybrid Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 694 ◽  
Author(s):  
Alqahtani ◽  
Aydi ◽  
Karapınar ◽  
Rakočević
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Linear Type ◽  
Linear And Nonlinear ◽  
Nonlinear Contractions ◽  
Type Contraction

In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.

scholarly journals Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
H. M. Srivastava ◽  
Sachin V. Bedre ◽  
S. M. Khairnar ◽  
B. S. Desale
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Lower Solution ◽  
Linear Spaces ◽  
Partially Ordered ◽  
Normed Linear Spaces ◽  
Monotonicity Conditions

Some hybrid fixed point theorems of Krasnosel’skii type, which involve product of two operators, are proved in partially ordered normed linear spaces. These hybrid fixed point theorems are then applied to fractional integral equations for proving the existence of solutions under certain monotonicity conditions blending with the existence of the upper or lower solution.

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 A common fixed point theorem for cyclic operators on partial metric spaces

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 407-414 ◽  
Author(s):  
Erdal Karapınar ◽  
Nabi Shobkolaei ◽  
Shaban Sedghi ◽  
Mansour Vaezpour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Cyclic Operators ◽  
Common Fixed Point Theorem

In this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.

scholarly journals On the existence and Ulam-Hyers stability of a new class of partial (Φ,χ)-fractional differential equations with impulses

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1977-1991
Author(s):  
Arjumand Seemab ◽  
ur Mujeeb Rehman ◽  
Michal Feckan ◽  
Jehad Alzabut ◽  
Syed Abbas
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Stability Of Solutions ◽  
New Class ◽  
Fractional Differential ◽  
Partial Fractional Differential Equations

In this paper, we consider the newly defined partial (?,?)-fractional integral and derivative to study a new class of partial fractional differential equations with impulses. The existence and Ulam-Hyers stability of solutions for the proposed equation are investigated via the means of measure of noncompactness and fixed point theorems. The presented results are quite general in their nature and further complement the existing ones.

scholarly journals Nonlocal boundary value problems for integro-differential Langevin equation via the generalized Caputo proportional fractional derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bounmy Khaminsou ◽  
Chatthai Thaiprayoon ◽  
Jehad Alzabut ◽  
Weerawat Sudsutad
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Langevin Equation ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Langevin Equations ◽  
Paper Study ◽  
Integral Conditions ◽  
Existence And Stability

AbstractResults reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions. The main theorems are proved with the help of Banach’s, Krasnoselskii’s, and Schaefer’s fixed point theorems and Ulam’s approach. Finally, an example is given to demonstrate the applicability of our theoretical findings.

scholarly journals Solvability of a Parametric Fractional-Order Integral Equation Using Advance Darbo G-Contraction Theorem

Foundations ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 286-303
Author(s):  
Vishal Nikam ◽  
Dhananjay Gopal ◽  
Rabha W. Ibrahim
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Numerical Solutions ◽  
Applied Mathematics ◽  
Fractional Integrals ◽  
Local Conditions ◽  
Contraction Theorem ◽  
Fractional Integral Equation

The existence of a parametric fractional integral equation and its numerical solution is a big challenge in the field of applied mathematics. For this purpose, we generalize a special type of fixed-point theorems. The intention of this work is to prove fixed-point theorems for the class of β−G, ψ−G contractible operators of Darbo type and demonstrate the usability of obtaining results for solvability of fractional integral equations satisfying some local conditions in Banach space. In this process, some recent results have been generalized. As an application, we establish a set of conditions for the existence of a class of fractional integrals taking the parametric Riemann–Liouville formula. Moreover, we introduce numerical solutions of the class by using the set of fixed points.

scholarly journals Nonlinear Caputo Fractional Derivative with Nonlocal Riemann-Liouville Fractional Integral Condition Via Fixed Point Theorems

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 829 ◽  
Author(s):  
Piyachat Borisut ◽  
Poom Kumam ◽  
Idris Ahmed ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Supremum Norm ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): c D 0 + q u ( t ) = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , u ( k ) ( 0 ) = ξ k , u ( T ) = ∑ i = 1 m β i R L I 0 + p i u ( η i ) , where n - 1 < q < n , n ≥ 2 , m , n ∈ N , ξ k , β i ∈ R , k = 0 , 1 , ⋯ , n - 2 , i = 1 , 2 , ⋯ , m , and c D 0 + q is the Caputo fractional derivatives, f : [ 0 , T ] × C ( [ 0 , T ] , E ) → E , where E is the Banach space. The space E is chosen as an arbitrary Banach space; it can also be R (with the absolute value) or C ( [ 0 , T ] , R ) with the supremum-norm. R L I 0 + p i is the Riemann–Liouville fractional integral of order p i > 0 , η i ∈ ( 0 , T ) , and ∑ i = 1 m β i η i p i + n - 1 Γ ( n ) Γ ( n + p i ) ≠ T n - 1 . Via the fixed point theorems of Krasnoselskii and Darbo, the authors study the existence of solutions to this problem. An example is included to illustrate the applicability of their results.

scholarly journals Some Fixed Point Theorems in -Metric Space Endowed with Graph

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Maria Samreen ◽  
Tayyab Kamran ◽  
Naseer Shahzad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contraction Mappings ◽  
Cyclic Operators

We define some notions of contraction mappings in -metric space endowed with a graph and subsequently establish some fixed point results for such classes of contractions. According to the applications of our results, we obtain fixed point theorems for cyclic operators and an existence theorem for the solution of an integral equation.

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