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THE REGULARIZED TRACE FORMULA FOR A DIFFERENTIAL OPERATOR WITH UNBOUNDED OPERATOR COEFFICIENT
E. Şen,A. Bayramov,K. Oruçoğlu 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.4
In this paper, rstly we investigated the spectrum and resolvent operator of a Sturm-Liouville type di¤erential operator. Finally we have obtained the regularized trace formula for di¤erential operator equation with unbounded operator coe¢ cient.
RESOLVENT DYNAMICAL SYSTEMS FOR MIXED VARIATIONAL INEQUALITIES
Muhammad, Aslan-Noor 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.1
In this paper, we suggest and analyze a class of resolvent dynamical systems associated with mixed variational inequalities. We study the globally asymptotic stability of the solution of the resolvent dynamical systems for the pseudomonotone operators. We also discuss some special cases, which can be obtained from our main results.
Park, Dong-Gun,Ahn, Young-Chel,Kwun, Young-Chel The Youngnam Mathematical Society Korea 2003 East Asian mathematical journal Vol.19 No.1
In this paper we prove the existence of mild and strong solutions of nonlinear delay integrodifferential equations with nonlocal conditions. The results are obtained by using the Schauder fixed point theorem and resolvent operator.
FINDING A ZERO OF THE SUM OF TWO MAXIMAL MONOTONE OPERATORS WITH MINIMIZATION PROBLEM
Abdallah Beddani 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.4
The aim of this paper is to construct a new method for finding the zeros of the sum of two maximally monotone mappings in Hilbert spaces. We will define a simple function such that its set of zeros coincide with that of the sum of two maximal monotone operators. Moreover, we will use the Newton-Raphson algorithm to get an approximate zero.In addition, some illustrative examples are given at the end of this paper.
SYSTEM OF GENERALIZED MULTI-VALUED RESOLVENT EQUATIONS: ALGORITHMIC AND ANALYTICAL APPROACH
Javad Balooee,Shih-sen Chang,Jinfang Tang Korean Mathematical Society 2023 대한수학회보 Vol.60 No.3
In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a P-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of H(·, ·)-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every H(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.
Junmin Chen,Xian Wang,Zhen He 영남수학회 2013 East Asian mathematical journal Vol.29 No.3
In this paper, a new monotonicity, M(·,·)-monotonicity, is introduced in Banach spaces, and the resolvent operator of an M(·,·)-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·,·)-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.
Chen, Junmin,Wang, Xian,He, Zhen The Youngnam Mathematical Society 2013 East Asian mathematical journal Vol.29 No.3
In this paper, a new monotonicity, $M({\cdot},{\cdot})$-monotonicity, is introduced in Banach spaces, and the resolvent operator of an $M({\cdot},{\cdot})$-monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with $M({\cdot},{\cdot})$-monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the convergence of the sequences generated by the proximal point algorithms in Banach spaces. The results in this paper extend and improve some known results in the literature.
Kim, Jong Kyu,Bhat, Muhammad Iqbal De Gruyter 2018 Demonstratio mathematica Vol.51 No.1
<P><B>Abstract</B></P><P>In this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces. We define the resolvent operator associated with A-monotone and H-monotone operators and prove its Lipschitz continuity. Using resolvent operator technique, we prove the existence and uniqueness of solution for this new system of variational inclusions. Moreover, we suggest an iterative algorithm for approximating the solution of this system and discuss the convergence analysis of the sequences generated by the iterative algorithm under some suitable conditions.</P>
Lan, Heng-You 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this work, by using Xu's inequality, Nalder's results, the notion of $(A,\;{\eta})-accretive$ mappings and the new resolvent operator technique associated with $(A,\;{\eta})-accretive$ mappings due to Lan et al., we study the existence of solutions for a new class of $(A,\;{\eta})-accretive$ variational inclusion problems with non-accretive set-valued mappings and the convergence of the iterative sequences generated by the algorithms in Banach spaces. Our results are new and extend, improve and unify the corresponding results in this field.
Nonexpansiveness of the resolvent average
Kum, S.,Lim, Y. Academic Press 2015 Journal of mathematical analysis and applications Vol.432 No.2
We show that the resolvent average for positive definite matrices, which interpolates between the harmonic and the arithmetic means, contracts the Thompson metric on the convex cone of positive definite matrices. Classical results depending on the nonexpansive property of the arithmetic average are considered in the context of the resolvent average. In particular, resolvent power mean approximation to the Karcher mean and Ferrante and Levy-like matrix equations are investigated.