• 제목/요약/키워드: resolvent operator

검색결과 76건 처리시간 0.027초

A SYSTEM OF VARIATIONAL INCLUSIONS IN BANACH SPACES

  • Liu, Zeqing;Zhao, Liangshi;Hwang, Hong-Taek;Kang, Shin-Min
    • East Asian mathematical journal
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    • 제26권5호
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    • pp.681-691
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    • 2010
  • A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

PARAMETRIC GENERALIZED MULTI-VALUED NONLINEAR QUASI-VARIATIONAL INCLUSION PROBLEM

  • Khan, F.A.;Alanazi, A.M.;Ali, Javid;Alanazi, Dalal J.
    • Nonlinear Functional Analysis and Applications
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    • 제26권5호
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    • pp.917-933
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    • 2021
  • In this paper, we investigate the behavior and sensitivity analysis of a solution set for a parametric generalized multi-valued nonlinear quasi-variational inclusion problem in a real Hilbert space. For this study, we utilize the technique of resolvent operator and the property of a fixed-point set of a multi-valued contractive mapping. We also examine Lipschitz continuity of the solution set with respect to the parameter under some appropriate conditions.

SOME SPECTRAL AND SCATTERING PROPERTIES OF GENERALIZED EIGENPARAMETER DEPENDENT DISCRETE TRANSMISSION STURM-LIOUVILLE EQUATION

  • Guher Gulcehre Ozbey;Guler Basak Oznur;Yelda Aygar ;Turhan Koprubasi
    • 호남수학학술지
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    • 제45권3호
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    • pp.457-470
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    • 2023
  • In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.

ITERATIVE ALGORITHMS WITH ERRORS FOR ZEROS OF ACCRETIVE OPERATORS IN BANACH SPACES

  • Jung, Jong-Soo
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.369-389
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    • 2006
  • The iterative algorithms with errors for solutions to accretive operator inclusions are investigated in Banach spaces, including a modification of Rockafellar's proximal point algorithm. Some applications are given in Hilbert spaces. Our results improve the corresponding results in [1, 15-17, 29, 35].

ITERATIVE ALGORITHMS FOR A SYSTEM OF RANDOM NONLINEAR EQUATIONS WITH FUZZY MAPPINGS

  • Kim, Jong Kyu;Salahuddin, Salahuddin
    • East Asian mathematical journal
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    • 제34권3호
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    • pp.265-285
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    • 2018
  • The main purpose of this paper, by using the resolvent operator technique associated with randomly (A, ${\eta}$, m)-accretive operator is to establish an existence and convergence theorem for a class of system of random nonlinear equations with fuzzy mappings in Banach spaces. Our works are improvements and generalizations of the corresponding well-known results.

GRAPH CONVERGENCE AND GENERALIZED CAYLEY OPERATOR WITH AN APPLICATION TO A SYSTEM OF CAYLEY INCLUSIONS IN SEMI-INNER PRODUCT SPACES

  • Mudasir A. Malik;Mohd Iqbal Bhat;Ho Geun Hyun
    • Nonlinear Functional Analysis and Applications
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    • 제28권1호
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    • pp.265-286
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    • 2023
  • In this paper, we introduce and study a generalized Cayley operator associated to H(·, ·)-monotone operator in semi-inner product spaces. Using the notion of graph convergence, we give the equivalence result between graph convergence and convergence of generalized Cayley operator for the H(·, ·)-monotone operator without using the convergence of the associated resolvent operator. To support our claim, we construct a numerical example. As an application, we consider a system of generalized Cayley inclusions involving H(·, ·)-monotone operators and give the existence and uniqueness of the solution for this system. Finally, we propose a perturbed iterative algorithm for finding the approximate solution and discuss the convergence of iterative sequences generated by the perturbed iterative algorithm.

VISCOSITY METHODS OF APPROXIMATION FOR A COMMON SOLUTION OF A FINITE FAMILY OF ACCRETIVE OPERATORS

  • Chen, Jun-Min;Zhang, Li-Juan;Fan, Tie-Gang
    • East Asian mathematical journal
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    • 제27권1호
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    • pp.11-21
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    • 2011
  • In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

ITERATIVE ALGORITHMS FOR A FUZZY SYSTEM OF RANDOM NONLINEAR EQUATIONS IN HILBERT SPACES

  • Salahuddin, Salahuddin
    • 대한수학회논문집
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    • 제32권2호
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    • pp.333-352
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    • 2017
  • In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.