In the framework of a b-metric space, by using the compatible and weak compatible conditions of selfmapping pair, we discussed the existence and uniqueness of the common fixed point for a class of φ-type contraction mapping, some new common fixed point theorems are obtained. In the end of the paper, we give some illustrative examples in support of our new results. The results presented in this ...

For a linear map from Mm to Mn, besides the usual positivity, there are two stronger notions, complete positivity and super-positivity. Given a positive linear map φ we study a decomposition φ = φ − φ with completely positive linear maps φ (j = 1, 2). Here φ + φ is of simple form with norm small as possible. The same problem is discussed with superpositivity in place of complete positivity.

Let X be a real Banach space with a normalized duality mapping uniformly norm-to-weak continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping JΦ with gauge φ. Let f be an α-contraction and {Tn} a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes xn+1 = αnf(xn) + (1− αn)Tnxn (1) with a general theorem a...

N be a rational map, where f 0 ,. .. , f N are homogeneous polynomials of degree d with no common factors. Then φ is defined at all points not in the indeterminacy locus Z(φ) = { P ∈ P N : f 0 (P) = · · · = f N (P) = 0 }. The map φ is said to be dominant if the image φ (P N Z(φ)) is Zariski dense, i.e., does not lie in a proper algebraic subset of P N. Alternatively, the map φ is dominant if th...

Abstract Let $\mathcal {A} \subset{\mathcal {B}}(\mathcal {H})$ A ⊂ B ( H ) be a row contraction and $\Phi _{\mathcal {A}}$ Φ determined by {A}$ completely positive map on ${\mathcal . ...

In this paper,  we introduce the notion of  generalized multivalued  $F$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.

Let C be an additive subgroup of Z n 2k for any k ≥ 1. We define a Gray map Φ : Z n 2k −→ Z kn 2 such that Φ(C) is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover, Φ is the unique Gray map such that Φ(C) is Hamming-compatible group code. Using this Gray map we discuss about the nonexistence of 1-perfect binary mixed group code.

Proof. First note that the map φ is uniquely determined by its components φ11, φ12, φ21, φ22. Indeed, by the universal property of the coproduct M1 ⊕ M2 we see that φ is uniquely determined by the maps φ∗1 := φ◦ι1 and φ∗2 := φ◦ι2. Then from the universal property of the product N1⊕N2 we see that the map φ∗1 is uniquely determined by the maps φ11 = π1 ◦φ∗1 and φ21 = π2 ◦ φ∗1. Similarly, φ∗2 is u...