Sentence examples for introduced the classes from inspiring English sources

Ma and Minda [1] gave a unified presentation of these classes and introduced the classes (1.2).

Levin and Lubinsky introduced the classes L ( C 2 ) and L ( C 2 + ) as analogies of the classes F ( C 2 ) and F ( C 2 + ) defined on I * = ( - d, d ).

Motivated by works of Kanas and Wiśniowska [10] and [11], Al-Kharsani and Al-Hajiry [13] introduced the classes k-uniformly convex functions and k-starlike functions of order η ( 0 ≤ η < 1 ) as below: k - UCV : = { f ∈ S : ℜ ( 1 + z f ″ ( z ) f ′ ( z ) − η ) > k | z f ″ ( z ) f ′ ( z ) | ( z ∈ U ) } (1.12).

Finally, we will prove the results for the various weighted -norms of, that is, Theorems 1.8, 1.9, and 1.10, in Section 4. Levin and Lubinsky introduced the classes and as an analogy of the classes and which they already defined on.

In [2], Definetti introduced the class of quasi-convex functions.

Iscan [8] introduced the class of harmonic convex functions.

Recently, in [1] the authors introduced the class of simulation functions as follows.

In 1996, Liu [6] introduced the class of κ-strictly asymptotically pseudocontractive mappings in Hilbert spaces.

In 1972, Goebel and Kirk [1] introduced the class of asymptotically nonexpansive self-mappings.

Recently, Khan et al. [29] introduced the class of subcompatible mappings as follows: Definition 2.1.

In 2012, Samet et al. [8] introduced the class of α-admissible mappings.