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The existence of a solution, convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in Banach spase $B$ are investigated. All the objects of the…
This manuscript is concerned with the approximate controllability of fractional nonlinear differential equations with nonlocal conditions of order $1<q<2$ in Banach spaces. As far as we know, few articles have investigated this issue. The…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen…
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-for solution of the considered nonlinear operator equation…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
In this paper, by employing fixed-point methods, we obtain the existence and uniqueness results for the nonlinear implicit fractional differential equations in Banach spaces. Further, we obtain the uniqueness, dependence of the solution on…
By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…
This paper deals with a general form of variational problems in Banach spaces which encompasses variational inequalities as well as minimization problems. We prove a characterization of local error bounds for the distance to the…
Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…
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…
We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified in assumption that the…
The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…