On Recent Results Concerning F-Contraction in Generalized Metric Spaces

Vujaković, Jelena; Mitrovic, S.; Pavlovic, Mladen; Radenović, Stojan

doi:10.3390/math8050767

Cited by 18 publications

(15 citation statements)

References 21 publications

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“…More details on partial metric and metric-like spaces can be found in ( [5][6][7]11,[13][14][15][16][17][18]), and information on other classes of generalized metric spaces and contractive mappings can be found in: ( [1,).…”

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

On ${\mathcal{F}}$-Contractions for Weak α-Admissible Mappings in Metric-Like Spaces

Vujaković¹,

Mitrovic

Mitrović

et al. 2020

Mathematics

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In the paper, we consider some fixed point results of F-contractions for triangular α-admissible and triangular weak α-admissible mappings in metric-like spaces. The results on F-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property (F1) of the strictly increasing mapping F:0,+∞→−∞,+∞. Our approach gives a proper generalization of several results given in current literature.

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Section: Definitionmentioning

confidence: 99%

“…d ml ξ n(k)+q , ξ m(k)+1 also converge to ε when k → +∞, where q ∈ N. For more details on (i)-(vi), the reader can see in ([26,27,36]). The concept of F -contraction was introduced by Wardowski in [16] (for more details, see also: [5,9,[14][15][16][17][18]24,28,[31][32][33]).…”

Section: Remarkmentioning

confidence: 99%

On ${\mathcal{F}}$-Contractions for Weak α-Admissible Mappings in Metric-Like Spaces

Vujaković¹,

Mitrovic

Mitrović

et al. 2020

Mathematics

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“…Since 2012., several research papers (for example [4][5][6][7][8][9][10][11][12][13][14][15][16]) considered a new type of contraction mapping introduced by Wardowski [17] . For other new-old types of contractive mappings see e.g., [18][19][20][21][22].…”

Section: Remarkmentioning

confidence: 99%

“…Recently, in [14], we proved the Theorem 4 using only the condition (F1) and the following two lemmas [9,10] . Lemma 1.…”

Section: Remarkmentioning

confidence: 99%

On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Vujaković¹,

Ljajko²,

Radojević

et al. 2020

Symmetry

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Many authors used the concept of F−contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

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“…Lately, fixed point theory has become the focus of many researchers and that is due to its applications in many fields, such as engineering and computer sciences. Also fixed point theory can be used to solve differential equations along with integral equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. M-metric spaces were introduced by Asadi, Karapinar and Salimi, in [15], they are an extension of a partial metric space.…”

Section: Introductionmentioning

confidence: 99%