• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1021-1034
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• 2021

This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.79-91
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• 2010

In this paper, a class of fractional integrodifferential equations of mixed type with nonlocal conditions is considered. First, using contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. Second, the existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with nonlocal conditions is also presented.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.793-809
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• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• East Asian mathematical journal
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• v.34 no.5
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• pp.651-660
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• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.51-65
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• 2019

In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of nonlinear fractional dynamic equations of order ${\alpha}$ (1 < ${\alpha}$ < 2). By using the Krasnoselskii's fixed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided f (t, 0) = 0, which include and improve some related results in the literature.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.669-681
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• 2001

This paper introduces the notions of essential and inessential map for countably $textsc{k}$-set contractive maps. These ideas enable us to establish a Krasnoselskii-Petryshyn compression and expansion theorem in a cone for countably $textsc{k}$-set contractive maps.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.255-268
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• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1205-1213
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• 2005

Applying a fixed point theorem for compact admissible maps due to Gorniewicz, we prove that under certain conditions each count ably condensing admissible maps in Frechet spaces has a positive eigenvalue. This result has many consequences, including the well-known theorem of Krasnoselskii.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.393-418
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• 2024

In this paper, we propose a new inertial subgradient extragradient algorithm with a new linesearch technique that combines the inertial subgradient extragradient algorithm and the KrasnoselskiiMann algorithm. Under some suitable conditions, we prove a weak convergence theorem of the proposed algorithm for finding a common element of the common solution set of a finitely many variational inequality problem and the fixed point set of a nonexpansive mapping in real Hilbert spaces. Moreover, using our main result, we derive some others involving systems of variational inequalities. Finally, we give some numerical examples to support our main result.