Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

In this paper, we establish some new existence, uniqueness and Ulam-Hyers stability theorems for coincidence problems for two single-valued mappings. The main results of this paper extend the results presented in O. Mleşniţe: Existence and Ulam-Hyers stability results for coincidence problems, J. Nonlinear Sci. Appl., 6 (2013), 108-116. In the last section two examples of application of these results are also given.

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“…In [4] it was proved that f is not a contraction but it is a separated contraction, taking ϕ : R+ → R+ defined by…”

Section: Preparatory Resultsmentioning

confidence: 99%

Coincidence problems for generalized contractions

Falset

Mleşniţe

2014

APPL ANAL DISCRETE M

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“…The existence of fixed points for the sum of two deterministic operators has attracted tremendous interest, and their applications are frequent in nonlinear analysis. Many improvements of Krasnosel'skii's theorem have been established in the literature over the course of time by modifying the above assumptions; see, for example, [14,15] and the references therein. Recently, Rao [5] obtained a probabilistic version of the Krasnosel'skii's theorem that involves the sum of a contraction random operator and a compact random operator on a closed convex subset of a separable Banach space.…”

Section: 1)mentioning

confidence: 99%

Some Krasnosel’skii type random fixed point theorems

2017

J. Nonlinear Funct. Anal.

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Abstract. The authors prove some random fixed point theorems for the sum of a weakly-strongly continuous random operator and an expansive random operator in Banach spaces. They also establish a random multivalued version of a Krasnosel'skii type fixed point theorem for the sum B + G, where B is a linear or nonlinear random operator and G is a random multivalued operator. They apply their results to a random fractional integral inclusion.A result for systems is also given. Their results extend previous ones in the literature.

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“…In the following, we state the Krasnoselskii fixed-point theorem, which is used to prove another existence theorem for solutions of the boundary value problem (1.1). [18,19]) Let be a closed convex and nonempty subset of a Banach space X. Let A, B be the operators such that (i) Ax C By 2 whenever x, y 2 ; (ii) A is compact and continuous; and (iii) B is a contraction mapping.…”

Section: Lemma 25mentioning

confidence: 99%

Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations

Liu

Jia

2015

Math. Meth. Appl. Sci.

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In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed‐point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd.

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Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

Cited by 47 publications

References 15 publications

Coincidence problems for generalized contractions

Coincidence problems for generalized contractions

Some Krasnosel’skii type random fixed point theorems

Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations

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