Auto-encoder is a special kind of neural network based on reconstruction. De-noising auto-encoder (DAE) is an improved auto-encoder which is robust to the input by corrupting the original data first and then reconstructing the original input by minimizing the reconstruction error function. And contractive auto-encoder (CAE) is another kind of improved auto-encoder to learn robust feature by int...

In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We f...

Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.

In this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. The first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. They improve thecorresponding  conclusions in the literature.

holds for all p, qEX (for all p, q with d(p, q) <e). Mappings, as above, satisfying (1) with the strict inequality sign for all p, qEX, pT^q (for all p, q with 0 <d(p, q) <e) are called contractive (e-contractive). A point yE Y EX is said to belong to the/-closure of Y, yE Y1, if /(F) C F and there is a point r¡E Y and a sequence {re,} of positive integers, («i<re2< • • ■ <Ui< ■ • ■ ), so that ...