Let f(t) be a real continuous function on an interval, and consider the operator function f(X) defined for Hermitian operators X. We will show that if f(X) is increasing w.r.t. the operator order, then for F (t) = ∫ f(t)dt the operator function F (X) is convex. Let h(t) and g(t) be C1 functions defined on an interval I. Suppose h(t) is non-decreasing and g(t) is increasing. Then we will define ...

The existence of coincidence points and common fixed points for operators satisfying a Presić-Kannan type contraction condition in a metric spaces setting is proved. A multi-step iterative method for constructing the common fixed points is also provided.

We prove that if A and B∗ are subnormal operators and X is a bounded linear operator such that AX −XB is a Hilbert-Schmidt operator, then f A X −Xf B is also a Hilbert-Schmidt operator and ‖f A X −Xf B ‖2 ≤ L‖AX −XB‖2 for f belongs to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and X ∈ L H is such that SX − XT belo...

This paper considers when one can invert general recursive operators which map a class of functions F to F . In this regard, we study four different notions of inversion. We additionally consider enumeration of operators which cover all general recursive operators which map F to F in the sense that for every general recursive operator Ψ mapping F to F , there is a general recursive operator in ...

the fixed point alternative methods are implemented to givehyers-ulam  stability for  the quintic functional equation $ f(x+3y)- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and thesextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$   in the setting ofintuitionistic fuzzy normed spaces (ifn-spaces).  this methodintroduces a met...

The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Walsh-Kaczmarz-Fourier series is of weak type (1,1) . Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Kaczmarz-Fourier series is of weak type (1,1) , provided that the supremum in the maximal operator is...

The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor’s entries denote the parity of the number of edges in subgraphs induced by r distinct vertices. For r = 2, it is the adjacency matrix with 1’s for edges and −1’s for nonedges. It is well-known that the 2-norm of the adjacency matrix of a random graph is O( √ n). Here we show that the 2-norm of the r-par...

We consider the operator A0f = (−1)n 1 v(t) ( Dρ )∗ [ u(t)Dρ ( f (t) v(t) )] , where Dρ f (t) = dk dtk [ ρ(t) dmf (t) dtm ] , ( Dρ )∗ f (t) = dm dtm [ ρ(t) dkf (t) dtk ] , k + m = n. Our main aim is to prove some spectral properties of a natural extension of this operator. In order to prove this we need to prove some properties of a function space, connected to the operator Dρ , and some embedd...

In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: −M(Du) + |u|u = f(x) in IR, where s > 1 and f satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality s...