Related papers: The generalized Newton--Kantorovich method for equ…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…
We obtain solutions of the nonlinear degenerate parabolic equation \[ \frac{\partial \rho}{\partial t} = {div} \Big\{\rho \nabla c^\star [ \nabla (F^\prime(\rho)+V) ] \Big\} \] as a steepest descent of an energy with respect to a convex…
In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
The authors introduce generalized Campanato space with regularized condition over non-homogeneous space, and study its basic properties including the John-Nirenberg inequality and equivalent characterizations. As applications, the…
We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups $\Gamma_0(N)$. Our main theorem unifies various results from the literature, and its significance is illustrated through the…
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defined in such a way that the wealth of techniques developed…
We investigate a limiting procedure for extending local integral operator equalities to the global ones and to applying it to obtaining generalizations of the Newton-Leibnitz formula for operator-valued maps for a wide class of unbounded…
Convergence rates results for Tikhonov regularization of nonlinear ill-posed operator equations in abstract function spaces require the handling of both smoothness conditions imposed on the solution and structural conditions expressing the…
The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of…
In this article, we obtain a version of the noncommutative Banach Principle suitable to prove Wiener-Wintner type results for weights in W1-space. This is used to obtain noncommutative Wiener-Wintner type ergodic theorems for various types…
In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations…
In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additional results address statements in higher order arithmetic…
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…
In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…
We take a Hamiltonian-based perspective to generalize Nesterov's accelerated gradient descent and Polyak's heavy ball method to a broad class of momentum methods in the setting of (possibly) constrained minimization in Euclidean and…
Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and…
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…
Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse…
Oscillatory second order linear ordinary differential equations arise in many scientific calculations. Because the running times of standard solvers increase linearly with frequency when they are applied to such problems, a variety of…