This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=\frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions zero order in the complex plane $\mathbb{C}$. We give logarithmic lemma, second fundamental theorem, defect relation, Picard theorem and five-value sense $q$-difference operator. By using this theory, we investigate growth entire solutions line...

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

We prove that for compatible weakly nonlocal Hamiltonian and symplectic operators, hierarchies of infinitely many commuting local symmetries and conservation laws can be generated under some easily verified conditions no matter whether the generating Nijenhuis operators are weakly nonlocal or not. We construct a recursion operator of the two dimensional periodic Volterra chain from its Lax repr...

In this paper, we present a study on mean square approximate controllability and finite-dimensional exact for the system governed by linear/semilinear infinite-dimensional stochastic evolution equations. We introduce resolvent-like operator and, using operator, formulate criterion finite-approximate of linear systems. A control is also found that provides in addition to requirement controllabil...

We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always w *-continuous on dual operator spaces. For example, this yields a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) ...

In this article, we present a sparse vector learning algorithm for ontology similarity measure and ontology mapping by virtue of accelerated first-order technology. The main procedure of our iterative algorithm is relying on proximity operator computation, Picard-Opial process and accelerated first-order tricks. The simulation experimental results show that the new proposed algorithm has high e...

Abstract This paper discusses different types of Ulam stability first-order nonlinear Volterra delay integro-differential equations with impulses. Such allow the presence two kinds memory effects represented by and kernel used fractional integral operator. Our analysis is based on Pachpatte’s inequality fixed point approach Picard operators. Applications are provided to illustrate results obtai...