Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

Cherichi, Meryam; Samet, Bessem; Vetro, Calogero

doi:10.1155/2013/293101

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…Frigon [14] and Chis and Precup [10] generalized the Banach contraction principle on gauge spaces. Some interesting results are also been obtained by the authors: Agarwal et al [1], Chifu and Petrusel [9], Cherichi et al [8,7], Lazara and Petrusel [18], Jleli et al [16].…”

Section: Introductionmentioning

confidence: 64%

Fixed point theorems for multivalued G-contractions in Hausdorff b-Gauge spaces

Ali¹,

Kamran²,

Postolache³

2015

J. Nonlinear Sci. Appl.

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Section: Introductionmentioning

confidence: 64%

Fixed point theorems for multivalued G-contractions in Hausdorff b-Gauge spaces

Ali¹,

Kamran²,

Postolache³

2015

J. Nonlinear Sci. Appl.

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“…al. [4], Frigon [5], Chis and Precup [6], Chifu and Petrusel [7], Lazara and Petrusel [8], Cherichi et al [9,10] and Jleli et al [11].…”

Section: Introductionmentioning

confidence: 99%

Some periodic and fixed point theorems on quasi-b-gauge spaces

et al. 2022

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The notions of a quasi-b-gauge space $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) and a left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family of generalized quasi-pseudo-b-distances generated by $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) are introduced. Moreover, by using this left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family, we define the left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -sequential completeness, and we initiate the Nadler type contractions for set-valued mappings $T:U\rightarrow Cl^{\mathcal{J}_{s ; \Omega }}(U)$ T : U → C l J s ; Ω ( U ) and the Banach type contractions for single-valued mappings $T: U \rightarrow U$ T : U → U , which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

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“…For instance, Frigon [9] and Chis and Precup [10] gave a generalization of the Banach contraction principle on gauge spaces. In the same direction, many interesting results have been raised obtained by different authors in [11][12][13][14][15][16][17]. In 2013, Ali et al [18] ensured the existence of fixed points for an integral operator via a fixed-point theorem on complete gauge spaces.…”

Section: Introductionmentioning

confidence: 99%