It is conceivable that the irregular mapping optimization of N(N>2) mappings may achieve a better error performance than the irregular mapping optimization of two mappings, which is not discussed in this paper and is currently under investigation.
Kohsaka and Takahashi [17] introduced a class of mappings which is called nonspreading mapping.
In order to explain this better, we give the following example [36] of relatively quasi-nonexpansive mappings which is not relatively nonexpansive mapping.
In 1981, Heilpern [2] used the concept of fuzzy sets and introduced a class of fuzzy mappings, which is a generalization of the set-valued mapping, and proved a fixed point theorem for fuzzy contraction mappings in metric linear spaces.
We observe that the algorithms in [13 16] involves the W-mapping generated by a family of infinitely (finitely) nonexpansive mappings which is an effective tool in nonlinear analysis (see [20, 21]).
Other tools rely on handcrafting the schema mappings, which is not appealing at all.
But, there exists a nonlinear continuous asymptotically quasi -nonexpansive mappings which is asymptotically -nonexpansive.
Let ℛ be the above class of mappings which is a generator of ⪯ ˜.
The following statement is a special case of Hopf's theorem for mappings, which is employed to prove Theorem 2.1.
then and are said to be a couple of quasicontractive mappings which is studied by Rhoades [5].
We prove a new strong convergence theorem for the mappings, which is an extension of results of [11].
