Sentence examples for modified the notions from inspiring English sources

Very recently Salimi et al. [14] modified the notions of α-admissible and α-ψ-contractive mappings as follows.

More recently, Salimi et al. [10] modified the notions of α-ψ-contractive and α-admissible mappings and established fixed point theorems to modify the results in [9].

Salimi et al. [8] modified the notions of α-ψ-contractive and α-admissible self-mappings by introducing another function η and established some fixed-point theorems for such mappings in complete metric spaces.

More recently, Salimi et al. [24] modified the notions of α-ψ-contractive and α-admissible mappings and established fixed point theorems which are proper generalizations of the recent results in [22, 23].

Afterwards Salimi et al. [18] and Hussain et al. [19, 20] modified the notions of α-ψ-contractive and α-admissible mappings and established certain fixed point theorems (see also [21 25]).

We say that T is called α ∗ -admissible whenever α ( x, y ) ≥ 1 implies that α ∗ ( T x, T y ) ≥ 1. Very recently Hussain et al. [12] modified the notions of α ∗ -admissible and α ∗ -ψ-contractive mappings as follows: Definition 6 Let T : X → 2 X be a multifunction, α, η : X × X → R + be two functions where η is bounded.

In [19], Saadati et al. have modified the notion of IFNSs of Saadati and Park [18].

Successively, George and Veeramani [28] slightly modified the notion of a fuzzy metric space introduced by Kramosil and Michálek.

More recently Salimi et al. [Fixed Point Theory Appl., 2013:151] modified the notion of α-ψ-contractive mappings.

More recently Salimi et al. (Fixed Point Theory Appl. 2013:151, 2013) modified the notion of α-ψ-contractive mappings and established certain fixed point theorems.

Later on, George and Veeramani [3] modified the notion of fuzzy metric spaces due to Kramosil and Michalek [2] and studied a Hausdorff topology of fuzzy metric spaces.