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Enlarging the ball of convergence of secant-like methods for non-differentiable operators
IOANNISK.ARGYROS,Hongmin Ren 대한수학회 2018 대한수학회지 Vol.55 No.1
In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using $\omega$-condition and centered-like $\omega$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.
ENLARGING THE BALL OF CONVERGENCE OF SECANT-LIKE METHODS FOR NON-DIFFERENTIABLE OPERATORS
Argyros, Ioannis K.,Ren, Hongmin Korean Mathematical Society 2018 대한수학회지 Vol.55 No.1
In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.
Kim, I.,Kim, K.H.,Lim, S. Academic Press 2016 Journal of mathematical analysis and applications Vol.436 No.2
<P>In this paper we prove a parabolic version of the Littlewood-Paley inequality for a class of time-dependent local and non-local operators of arbitrary order, and as an application we show that this inequality gives a fundamental estimate for an L-p-theory of high-order stochastic partial differential equations. (C) 2015 Elsevier Inc. All rights reserved.</P>
Uday Chand De,Mohammad Nazrul Islam Khan 대한수학회 2023 대한수학회논문집 Vol.38 No.4
The aim of the present paper is to study complete lifts of a semi-symmetric non-metric connection from a Riemannian manifold to its tangent bundles. Some curvature properties of a Riemannian manifold to its tangent bundles with respect to such a connection have been investigated.
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments
Srivastava, Hari Mohan Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.1
The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.