A local and semi-local convergence is developed of a class iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions first-order divided differences. Special cases this method are well-known algorithms, in particular, Secant, Kurchatov, Steffensen as well Newton method. For analysis, we use technique recurrent fun...

Counting lattice points inside a ball of large radius in Euclidean space is classical problem analytic number theory, dating back to Gauss. We propose variation on this problem: studying the asymptotics measure an integer affine planes ball. The first term volume ball; we study size remainder term. While equivalent counting eigenvalues Laplace operator torus, our corresponds integrated density ...

In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively...

We prove a theorem that generalizes various results ([4, Theorem 1], [9, Theorem 1-8], [7], [8, Lemma 4.1]) concerning eigenvalues and spectral points in the boundary of the spatial numerical range and numerical range of a continuous linear operator T on a complex normed space X. The proof is similar to the proof of [4, Theorem 1] and uses a fixed point theorem as do the proofs of [4, Theorem 1...

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...

in this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{t}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. we use a strong convolution technique and derive inclusion results. a radius problem and some other interesting properties of these classes are discussed.

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...