Sentence examples for mappings and also from inspiring English sources

Qihou [28] extended Schu's result to the general setting of asymptotically demicontractive mappings and also obtained the strong convergence of Ishikawa iteration for asymptotically hemicontractive mappings.

Here we modify the result for Ćirić quasi-contraction-type mappings and also prove the same result by taking D-admissible mappings.

In 2003, Kirk et al. [1] introduced concepts of cyclic mappings and cyclic contraction mappings and also gave some interesting fixed point theorems for these mappings.

Recently, Vijayaraju [21] proved by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces.

In this paper, we introduce a new class of proximal contractions, which extends the class of weakly C-contractive mappings to the class of non-self mappings, and also give some examples to illustrate our main results.

Consequently, we prove the existence of a common fixed point for weakly compatible mappings and also Banach operator pairs which are -generalized contraction pairs (see Theorem 2.3 and Theorem 2.5).

Recently, Sadiq Basha in [26] gave necessary and sufficient conditions to claim the existence of a best proximity point for proximal contractions of the first kind and the second kind, which are non-self mapping analogues of contraction self-mappings, and also established some best proximity and convergence theorems.

Zhong and Huang [30] studied the solution stability of parametric weak vector variational inequalities in reflexive Banach spaces and obtained the lower semi-continuity of the solution mapping for the parametric weak vector variational inequalities with strictly C-pseudo-mapping and also proved the lower semi-continuity of the solution mapping by degree-theoretic method.

Recently, Sadiq Basha in [30] gave necessary and sufficient conditions to the claim of the existence of a best proximity point for proximal contractions of the first kind and the second kind which are non-self-mapping analogs of contraction self-mappings and also established some best proximity and convergence theorems.

As applications, we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings, and we also obtain random fixed point theorems.

Here, for our further use, we recall only the two fundamental notions of 'weakly compatible mappings' and 'property E.A'; see also [17, 18].