Coincidence and common fixed point theorems for four mappings satisfying (αs, F)-contraction

Notes on Some Recent Papers Concerning $F$-Contractions in $b$-Metric Spaces

“…In [12], the authors modified the previous definition, putting s 2 instead of 1 on the righthand sides of the respective inequalities (the idea was to use them for mappings acting in b-metric spaces with parameter s). However, it is clear that if one puts α 1 (x, y) = 1 s 2 α(x, y), all of their definitions reduce to the ones from [4].…”

“…Moreover, we will show that some conditions of admissibility, used in [12] and some other papers, can be replaced by easier ones.…”

“…Further, their approach was used in the papers [1,2,8,10,11,12,13,14,15,16] to obtain various fixed point results, mostly for multivalued mappings. However, as we are going to show using the following result, most of the conditions used in all these articles are too strong.…”

Some Existence Results for a System of Nonlinear Fractional Differential Equations

“…Recently, fixed point theory is being applied to show the existence of solutions of different mathematical models expressed in the forms of differential, integral, functional, fractional differential, and matrix equations (both linear and nonlinear). ere are several common fixed point theorems, in the literature, which generalize BCP and have been applied to show the existence of solutions of different mathematical models involving two or more functions (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], for details).…”

New fixed point results in quasi-metric spaces and applications in fractals theory

“…In this respect, Secelean and Wardowski [18] introduced ψF-contractions as being selfmappings T satisfying the inequality F(d(Tx, Ty)) ≤ ψ (F(d(x, y))) for all x, y ∈ X, Tx = Ty, where ψ : (-∞, μ) → (-∞, μ) is increasing and ψ n (t) → -∞ for all t ∈ (-∞, μ), μ = sup F. In the above mentioned paper, some fixed point results are given even if F does not satisfy all conditions (F1)-(F3). Very recently, Nazama, Arshada, and Postolache [19] gave some interesting results concerning coincidence and common fixed points for four mappings satisfying certain F-contraction type conditions. For other generalizations and applications of F-contractions, one can also see [20] and [21].…”