The Schauder and Krasnoselskii Fixed-Point Theorems on a Frechet Space

Arwadi, Toufic El; Cherif, Mohamed Amine

doi:10.1007/s00009-018-1141-9

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Toufic El Arwadiet al, [14] have presented some fixed-point theorems of theSchauder and Krasnoselskii type in a Frechet topological vector spaceE. Here,proves a fixed-point theorem which was for every weakly compactmap from a closed bounded convex subset of a Frechet topological vectorspace having the Dunford-Pettis property into itself has a fixed point.…”

Section: Schauder-tychonoffmentioning

confidence: 87%

Existence of solutions for fixed point theorem

.Malathi¹,

Chelliah²

2021

JUSST

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The development of a mathematical model based on diffusion has received a great dealof attention in recent years, many scientist and mathematician have tried to apply basicknowledge about the differential equation and the boundary condition to explain anapproximate the diffusion and reaction model. The subject of fractional calculus attracted much attentions and is rapidly growing area of research because of itsnumerous applications in engineering and scientific disciplines such as signal processing, nonlinear control theory, viscoelasticity, optimization theory [1], controlled thermonuclear fusion, chemistry, nonlinear biological systems, mechanics,electric networks, fluid dynamics, diffusion, oscillation, relaxation, turbulence, stochastic dynamical system, plasmaphysics, polymer physics, chemical physics, astrophysics, and economics. Therefore, it deserves an independent theoryparallel to the theory of ordinary differential equations (DEs).In the development of non-linear analysis, fixed point theory plays an important role. Also, it has been widely used in different branches of engineering and sciences. Banach fixed point theory is a essential part of mathematical analysis because of its applications in various area such as variational and linear inequalities, improvement and approximation theory. The fixed-point theorem in diffusion equations plays a significant role to construct methods to solve the problems in sciences and mathematics. Although Banach fixed point theory is a vast field of study and is capable of solving diffusion equations. The main motive of the research is solving the diffusion equations by Banach fixed point theorems and Adomian decomposition method. To analysis the drawbacks of the other fixed-point theorems and different solving methods, the related works are reviewed in this paper.

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Section: Schauder-tychonoffmentioning

confidence: 87%

Existence of solutions for fixed point theorem

.Malathi¹,

Chelliah²

2021

JUSST

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“…There are diverse extensions of Krasnosel'skii fixed point theorem in the literature, and the operator B is often required to be contractive or expansive, or of any typical form involving control functions (see, e.g., [1,[3][4][5][6][7][8]14,17,19] and the references therein). There are also a few results related with Meir-Keeler-type conditions used in Krasnosel'skii fixed point theorem (see, e.g., [11]).…”

Section: Introductionmentioning

confidence: 99%

Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings

Pourhadi

Saadati

Kadelburg

2020

NAMC

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In this paper, inspired by the idea of Meir-Keeler contractive mappings, we introduce Meir-Keeler expansive mappings, say MKE, in order to obtain Krasnosel'skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir-Keeler mapping and expansive Krasnosel'skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel'skii fixed point theorems

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“…In the fixed point theory of continuous mappings, a well-known theorem of Banach [1] states that if (X, d) is a complete metric space and if S is a self-mapping on X which satisfies the inequality d(Sx, Sy) ≤ kd(x, y) for some k ∈ [0, 1) and all x, y ∈ X, then S has a unique fixed point x * and the sequence of successive approximations {Sx n } converges to x * for all x ∈ X, the Banach's theorem [1] has been extensively studied and generalized on many settings (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application

et al. 2019

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The purpose of this paper is to introduce the notion of generalized multivalued ψ , ϕ -type contractions and generalized multivalued ψ , ϕ -type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented.

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The Schauder and Krasnoselskii Fixed-Point Theorems on a Frechet Space

Cited by 3 publications

References 7 publications

Existence of solutions for fixed point theorem

Existence of solutions for fixed point theorem

Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings

Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application

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