Sentence examples for mappings generalizing the from inspiring English sources

An important class of mappings generalizing the class of nonexpansive mappings is the class of Lipschitz pseudocontractive maps.

One important (see, e.g., [[8], p.57]) class of nonlinear mappings generalizing the class of contraction mappings is the class of nonexpansive mappings.

An important class of asymptotically pseudocontractive mappings generalizing theclass of asymptotically nonexpansive mapping has been introduced and studied by Schuin 1991; see [19].

We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988).

A mapping T : C → C is called generalized hybrid if there exist α, β ∈ R such that α ∥ T x − T y ∥ 2 + ( 1 − α ) ∥ x − T y ∥ 2 ≤ β ∥ T x − y ∥ 2 + ( 1 − β ) ∥ x − y ∥ 2. for all x, y ∈ C. We note that the generalized hybrid mappings generalize several well-known mappings.

On the other hand, Verma [4, 5] introduced the concept of -monotone mappings, which generalizes the well-known general class of maximal monotone mappings and originates way back from an earlier work of the Verma [7].

The proved results using the concept of -admissible mappings generalize and extend various well-known results in the literature.

We call these mappings generalized multivalued nonexpansive mappings in the sense of Suzuki or multivalued mappings satisfying the condition.

Recently, Imdad and Soliman [15] introduced fixed point theorems for an asymptotically regular semigroup of uniformly generalized Lipschitzian mappings which generalize the results due to Jen-Chih Yao and Lu-Chuan Zeng [14].

Later on, Kirk and Xu [23] introduced the concept of asymptotic pointwise nonexpansive mappings which generalizes the concept of asymptotically nonexpansive mappings and proved the existence of fixed points for such maps in a uniformly convex Banach space.

As Verma point out "the class of -monotone mappings generalizes -monotone mappings.