Sentence examples for mappings for example from inspiring English sources

Note that the class of better admissible mapping includes many important classes of mappings, for example, the class in [18], in [19] and so on as proper subclasses.

Concretely, for one thing, from mappings, for example, the concept of a φ-contraction mapping was introduced in 1968 by Browder [4].

Concretely, for one thing, from mappings, for example, the concept of a Kannan contraction mapping was introduced in 1969 by Kannan [2] as follows: A self-map T on a metric space (( X,d )) is called a Kannan contraction mapping if there exists (kin[0,frac{1}{2})) such that d ( Tx,Ty ) leq k bigl[ d ( x,Tx ) +d ( y,Ty ) bigr],quad forall x,yin X.

Mann iteration algorithm has been extensively investigated for nonexpansive mappings, for example, please see [6, 7].

There is a wealth of results concerning this class of mappings (for example, see [28 32] and the references therein).

It is obvious that the class of relatively nonexpansive multivalued mappings contains properly the class of relatively nonexpansive multivalued mappings (for example, see [20]).

(b) The argument techniques in Theorems 3.1 and 3.2 are different from the ones in [[11], Theorems 3.1 and 3.2] and the ones in [[1], Theorems 5.2 and 6.1] because we use the properties of strict pseudocontractive mappings and maximal monotone mappings (see, for example, Lemmas 2.1, 2.4 and 2.6).

Is there some way to improve the results to more than two mappings or a family of mappings as in the case of nonexpansive mappings (see, for example, [10] and references contained therein)?

Questions (i) Are the results in Theorem 2.2 and Theorem 3.4 still true when the norm closedness for R c is replaced by weak closedness or weak∗ closedness (for dual Banach spaces)?   (ii) Is there some way to improve the results to more than two mappings or a family of mappings as in the case of nonexpansive mappings (see, for example, [10] and references contained therein)?  .

Results which had been known only for Hilbert spaces and Lipschitz mappings have been extended to more general Banach spaces and more general class of mappings; see, for example, [1 6] and the references therein for more information about this problem.

For results on the approximation of common fixed points of families of multi-valued nonexpansive mappings (see, for example, Abbas et al. [22]), and for multi-valued strictly pseudo-contractive mappings see, Chidume et al. [12], Chidume and Ezeora [23], Ofoedu and Zegeye [24], Panyanak [3], Shahzad and Zegeye [25] and the references therein.