A Perov type theorem for cyclic contractions and applications to systems of integral equations

Magdaş, Adrian

doi:10.18514/mmn.2017.1966

Cited by 2 publications

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“…R. George et al in [4] considered various types of cyclic contractions, such as Kannan, Chatterjee, andĆirić, and proved the existence and uniqueness theorems for these classes of operators. Other results that involve the notion of cyclic contraction, including applications to integral equations, can be found in [5][6][7][8]. We also note that the cyclic operator idea has been applied in deriving synchronisation conditions of complex dynamical systems-see [9].…”

Section: Introductionmentioning

confidence: 99%

Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Guran

Bota

2021

Symmetry

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The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

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Section: Introductionmentioning

confidence: 99%

Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Guran

Bota

2021

Symmetry

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Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

Bota¹,

Guran

2021

MATH

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<abstract><p>The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $ b $-metric spaces. The considered operators are generalized $ \varphi $-contractions and $ \alpha $-$ \varphi $ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.</p></abstract>

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A Perov type theorem for cyclic contractions and applications to systems of integral equations

Abstract: In this paper we will prove a fixed point theorem of Perov type for cyclic contractions on complete generalized metric spaces. Then, as an application, we will study the existence, uniqueness and approximation of the solution for a system of integral equations.

Cited by 2 publications

References 1 publication

Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

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