Existence of fixed points and measures of weak noncompactness

Garcia-Falset, Jesús

doi:10.1016/j.na.2009.01.096

Cited by 42 publications

(11 citation statements)

References 13 publications

(22 reference statements)

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“…These definitions slightly differ from and extend those of Garcia‐Falset . Fixed‐point results for such generalized contractions and expansions are collected in the following proposition.…”

Section: Fixed‐point Results For the Sum Operators T + Smentioning

confidence: 99%

“…X a mapping. T is called a p-˚-contraction if there are an integer p and 2˚such that d.T p x, T p y/ Ä .d.x, y// for all x, y 2 M; T is called a p-˚-expansion if there are an integer p and 2˚such that .d.T p x, T p y// d.x, y/ for all x, y 2 M. These definitions slightly differ from and extend those of Garcia-Falset [38,39]. Fixed-point results for such generalized contractions and expansions are collected in the following proposition.…”

Section: Corollary 27mentioning

confidence: 97%

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Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

Xiang

Georgiev

2015

Math Methods in App Sciences

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Communicated by W. SprößigIn this paper, we first establish some user-friendly versions of fixed-point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed-point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed-point theorem. Next, with these obtained fixed-point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra-type integral equations.

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Section: Fixed‐point Results For the Sum Operators T + Smentioning

confidence: 99%

Section: Corollary 27mentioning

confidence: 97%

Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

Xiang

Georgiev

2015

Math Methods in App Sciences

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“…Remark 3. 12 We note that Theorem 3.11 holds when we replace assumption (iv) by (iv) A(M) + B(M) ⊆ M. Indeed, it can be seen easily that (iv) implies that condition (iv) holds true. Next we show that I − (A + B) is demiclosed at zero.…”

Section: Remark 38mentioning

confidence: 87%

Krasnoselskii‐type fixed point theorems with applications to Hammerstein integral equations in spaces

Cai

2013

Mathematische Nachrichten

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“…Remark 2.7 Theorem 2.6 is a special case of Theorem 12 in [16], namely where the Banach space is C(K , X ).…”

Section: Then the Set Of Fixed Points Of F Is Non-empty And Weakly Cmentioning

confidence: 99%

On an integral equation under Henstock–Kurzweil–Pettis integrability

Amar

2015

Arab. J. Math.

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In this paper, we investigate the set of solutions for nonlinear Volterra type integral equations in Banach spaces in the weak sense and under Henstock-Kurzweil-Pettis integrability. Moreover, a fixed point result is presented for weakly sequentially continuous mappings defined on the function space C(K , X ), where K is compact Hausdorff and X is a Banach space. The main condition is expressed in terms of axiomatic measure of weak noncompactness. Mathematics Subject Classification

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Existence of fixed points and measures of weak noncompactness

Cited by 42 publications

References 13 publications

Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

Noncompact‐type Krasnoselskii fixed‐point theorems and their applications

Krasnoselskii‐type fixed point theorems with applications to Hammerstein integral equations in spaces

On an integral equation under Henstock–Kurzweil–Pettis integrability

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