Krasnosel’skii-type fixed point theorems for convex-power condensing mappings in locally convex spaces

Khchine, Abdelmjid; Maniar, Lahcen; Taoudi, Mohamed-Aziz

doi:10.1007/s11784-017-0465-6

Cited by 5 publications

(10 citation statements)

References 28 publications

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“…If T is p α −contraction mapping of K into itself, then T has a unique fixed point u in K and T n (x) −→ u as n −→ ∞ for each x ∈ K. Lemma 2.3. [11] Let (X, (p α ) α∈I ) be a sequentially complete Hausdorff locally convex space and K be a closed subset of X. Assume T : K −→ X is p α −expansive mapping and K ⊂ T(K).…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 2.12. [11] Let (X, (p α ) α∈I ) be a Hausdorff locally convex space and S : K −→ X be a p α -contraction with constant k α . Then for each α ∈ I, and for all bounded subset D of K we have…”

Section: Preliminariesmentioning

confidence: 99%

“…Recently, Khchine, Maniar and Taoudi [11] established a collection of new fixed point theorems for operators of the form T + S on an bounded convex K subset of a locally convex space (X, (p α ) α∈I ) where T is assumed to be p α −contraction (or p α −nonexpansive or p α −expansive) operator while S is assumed to be continuous and S is T−convex-power condensing about x 0 and n 0 ∈ N * w.r.t Φ (i.e., for any bounded set N of K with Φ(N) > 0, we have Φ(F (n 0 ,x 0 ) (T, S, N)) < Φ(N)…”

Section: Introductionmentioning

confidence: 97%

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Fixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application

Amar

Derbel

2020

Filomat

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In this paper, we introduce the concept of a countably asymptotically ?-nonexpansive operator. In addition, we establish new fixed point results for some countably asymptotically ?-nonexpansive and sequentially continuous maps, fixed-point results of Krasnosel?skii type in locally convex spaces. Moreover, we present Leray-Schauder-type fixed point theorems for countably asymptotically ?-nonexpansive maps in locally convex spaces. Apart from that we show the applicability of our results to the theory of Volterra integral equations in locally convex spaces. The main condition in our results is formulated in terms of the axiomatic measure of noncompactness. Our results improve and extend in a broad sense recent ones obtained in literature.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Fixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application

Amar

Derbel

2020

Filomat

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“…This notion was extended by Ezzinbi and Taoudi [4] and then by Shi [5]. Recently, Khchine et al [6] extended the view of a convex power condensing operator T in connection with another operator S of [5] in complete Hausdorff locally convex space. In particular, they relaxed the compactness condition in Krasnosel'skii fixed point theorem by using the notion of MNC.…”

Section: Introductionmentioning

confidence: 99%

Solution of infinite system of ordinary differential equations and fractional hybrid differential equations via measure of noncompactness

Zada

Sarwar

Nashine

2019

Journal of Taibah University for Science

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In this work, we use the notion of convex power condensing mapping under measure of noncompactness in locally convex spaces and establish some new coupled fixed point results. The results proved herein are the generalization and extension of some widely known results in the existing literature. Furthermore, we apply our results for the existence of solution to infinite system of ordinary differential equations and system of fractional hybrid differential equations.

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“…Let X be a nonempty bounded closed convex subset of a Banach space E and T : Ω × X ⟶ E and S : Ω × E ⟶ E be two random operators. Following [24,32,38], we set for any ω ∈ Ω and for any subset M of X:…”

mentioning

confidence: 99%

Random Fixed Point Theorems and Applications to Random First-Order Vector-Valued Differential Equations

El-Ghabi

Khchine

Taoudi

2021

Journal of Function Spaces

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In this paper, we establish several random fixed point theorems for random operators satisfying some iterative condition w.r.t. a measure of noncompactness. We also discuss the case of monotone random operators in ordered Banach spaces. Our results extend several earlier works, including Itoh’s random fixed point theorem. As an application, we discuss the existence of random solutions to a class of random first-order vector-valued ordinary differential equations with lack of compactness.

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Krasnosel’skii-type fixed point theorems for convex-power condensing mappings in locally convex spaces

Cited by 5 publications

References 28 publications

Fixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application

Fixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application

Solution of infinite system of ordinary differential equations and fractional hybrid differential equations via measure of noncompactness

Random Fixed Point Theorems and Applications to Random First-Order Vector-Valued Differential Equations

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