Crossover operator plays a crucial role in the efficiency of genetic algorithm (GA). Several crossover operators have been proposed for solving the travelling salesman problem (TSP) in the literature. These operators have paid less attention to the characteristics of the traveling salesman problem, and majority of these operators can only generate feasible solutions. In this paper, a crossover ...

Vector inequalities for powers of some operators in Hilbert spaces with applications for operator norm, numerical radius, commutators and selfcommutators are given.

Let A be a positive (semidefinite) bounded linear operator acting on complex Hilbert space \(\big ({\mathcal {H}}, \langle \cdot , \rangle \big )\). The semi-inner product \({\langle x, y\rangle }_A := Ax, \), \(x, y\in {\mathcal {H}}\) induces seminorm \({\Vert \Vert }_A\) \({\mathcal {H}}\). T an A-bounded {H}}\), the A-numerical radius of is given by $$\begin{aligned} \omega _A(T) = \sup \Bi...

The main goal of this article is to establish several new \({\mathbb {A}}\)-numerical radius equalities for \(n\times n\) circulant, skew imaginary tridiagonal, and anti-tridiagonal operator matrices, where {A}}\) the diagonal matrix whose entries are positive bounded A. Some special cases our results lead earlier works in literature, which shows that more general. Further, some pinching type i...

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

The Cauchy-Schwarz, Buzano and Kre\u{\i}n inequalities are three about inner product. main goal of this article is to present refinements Cauchy-Schwarz inequalities, a new proof refined version Kre\u{\i}n-type inequality. Applications that include Buzano-type for certain operators, operator norm numerical radius Hilbert space operators will be presented.

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...