On some F-contraction of Piri-Kumam-Dung-type mappings in metric spaces

Abstract

Introduction/purpose: This paper establishes some new results of Piri-Kumam-Dung-type mappings in a complete metric space.Тhe goal was to improve the already published results.
 Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence.
 Results: New results were obtained concerning the F - contraction mappings of in a complete metric space. To prove it, the authors used only property (W1).
 Conclusion: The authors believe that the obtained results represent a significant improvement of many known results in the existing literature.

New Results on F-Contractions in Complete Metric Spaces

“…Moreover, if the function F: (0, +∞) → (−∞, +∞) is non-decreasing then we conclude that there are lim r→ q − F( r) = F( q−) and lim r→ q + F( r) = F( q+). For more details on monotone functions, as well as on F-contractions, see [10][11][12][13][14][15][16][17][18][19][20].…”

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

“…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,).…”

“…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]).…”

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

“…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].…”