Switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives

<abstract><p>In this paper, we consider switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam-Hyers-Rassias stability of our proposed model, with the help of generalized Diaz-Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.</p></abstract>

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Fixed point theorems for non-self maps I

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171294001018 ◽

1994 ◽

Vol 17 (4) ◽

pp. 713-716 ◽

Cited By ~ 1

Author(s):

Troy L. Hicks ◽

Linda Marie Saliga

Keyword(s):

Fixed Point ◽

Metric Space ◽

Closed Subset ◽

Fixed Point Theorems ◽

Complete Metric Space ◽

Sufficient Conditions ◽

General Setting ◽

Necessary And Sufficient Conditions ◽

Necessary And Sufficient

Supposef:C→XwhereCis a closed subset ofX. Necessary and sufficient conditions are given forfto have a fixed point. All results hold whenXis complete metric space. Several results hold in a much more general setting.

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Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0240 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Rizwan Rizwan ◽

Akbar Zada ◽

Hira Waheed ◽

Usman Riaz

Keyword(s):

Functional Analysis ◽

Fixed Point ◽

Fractional Order ◽

Coupled System ◽

Langevin Equations ◽

Nonlinear Functional Analysis ◽

Nonlinear Functional ◽

Proposed Model ◽

Ulam’S Type Stability ◽

Stability Results

Abstract In this manuscript, switched coupled system of nonlinear impulsive Langevin equations involving four Hilfer fractional-order derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss the existence, uniqueness, and Ulam’s type stability results of our proposed model, with the help of Schaefer’s fixed point theorem. An example is provided at the end to illustrate our results.

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Stability of Picard operators under operator perturbations

Annals of West University of Timisoara - Mathematics and Computer Science ◽

10.2478/awutm-2018-0012 ◽

2018 ◽

Vol 56 (2) ◽

pp. 3-12

Author(s):

Adrian Petruşel ◽

Ioan A. Rus

Keyword(s):

Banach Space ◽

Fixed Point ◽

Metric Space ◽

Unique Fixed Point ◽

Complete Metric Space ◽

Sufficient Conditions ◽

Picard Operator

AbstractIn this paper we study the following problems: I. Let (M, d) be a complete metric space and f, g : M → M be two operators. We suppose that:(a) f is a Picard operator with its unique fixed point x *f;(b) there exists η > 0 such that d(f(x), g(x)) ≤ η, for every x ∈ M.The problem consists in estimating d(gn(x), x*f), for x ∈ M and n ∈ 𝕅*.II. Let B be a Banach space and f, g : B → B be two operators. We suppose that f is a Picard operator. The problem is to find sufficient conditions which guarantee that f + g is a Picard operator.

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On Fixed Point Theorems in Complete Metric Space

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/1128 ◽

2019 ◽

Vol 10 (7) ◽

pp. 1419-1425

Author(s):

Jayashree Patil ◽

Basel Hardan

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Complete Metric Space

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Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽

10.3390/sym13030501 ◽

2021 ◽

Vol 13 (3) ◽

pp. 501

Author(s):

Ahmed Boudaoui ◽

Khadidja Mebarki ◽

Wasfi Shatanawi ◽

Kamaleldin Abodayeh

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fixed Points ◽

Metric Space ◽

Fixed Point Theorems ◽

Coupled Fixed Point ◽

Sufficient Conditions ◽

Impulsive Differential Equations ◽

System Of Differential Equations ◽

Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

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Convergence of successive approximations to a stochastic fixed point

Journal of Applied Probability ◽

10.2307/3212950 ◽

1980 ◽

Vol 17 (1) ◽

pp. 297-299

Author(s):

Arun P. Sanghvi

Keyword(s):

Fixed Point ◽

Common Fixed Point for Generalized Bose-Mukherjee-Type Fuzzy Mappings

ISRN Applied Mathematics ◽

10.1155/2013/935386 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Ming-liang Song ◽

Zhong-qian Wang

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Common Fixed Point ◽

Point Theorem ◽

Metric Space ◽

Complete Metric Space ◽

Common Fixed Point Theorem

We prove a common fixed point theorem for a pair of generalized Bose-Mukherjee-type fuzzy mappings in a complete metric space. An example is also provided to support the main result presented herein.

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Fixed Point Theorems for Generalized αs-ψ-Contractions with Applications

Journal of Function Spaces ◽

10.1155/2018/8368546 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

Zhenhua Ma ◽

Muhammad Nazam ◽

Sami Ullah Khan ◽

Xiangling Li

Keyword(s):

Fixed Point ◽

Boundary Value Problems ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Elliptic Boundary ◽

Sufficient Conditions ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Unique Common Fixed Point

We study the sufficient conditions for the existence of a unique common fixed point of generalized αs-ψ-Geraghty contractions in an αs-complete partial b-metric space. We give an example in support of our findings. Our work generalizes many existing results in the literature. As an application of our findings we demonstrate the existence of the solution of the system of elliptic boundary value problems.

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Suzuki ψF-contractions and some fixed point results

Carpathian Journal of Mathematics ◽

10.37193/cjm.2018.01.10 ◽

2018 ◽

Vol 34 (1) ◽

pp. 93-102

Author(s):

NICOLAE-ADRIAN SECELEAN ◽

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Space ◽

Metric Spaces ◽

Complete Metric Space ◽

Continuity Point ◽

Picard Operator ◽

Nonlinear Anal ◽

New Type

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.

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On a theorem of Brian Fisher in the framework of w-distance

Carpathian Journal of Mathematics ◽

10.37193/cjm.2017.02.07 ◽

2017 ◽

Vol 33 (2) ◽

pp. 199-205

Author(s):

DARKO KOCEV ◽

◽

VLADIMIR RAKOCEVIC ◽

Keyword(s):

Fixed Point ◽

Metric Space ◽

Metric Spaces ◽

Fixed Point Theory ◽

Complete Metric Space ◽

Point Theory ◽

Common Fixed Points ◽

Complete Metric Spaces ◽

Condition C ◽

Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

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