• Title/Summary/Keyword: Generalized resolvent

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ON GENERALIZED NONLINEAR QUASIVARIATIONAL INEQUALITIES

  • Li, Jin-Song;Kang, Shin-Min
    • East Asian mathematical journal
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    • v.25 no.2
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    • pp.141-146
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    • 2009
  • In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a xed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.

SYSTEM OF GENERALIZED NONLINEAR MIXED VARIATIONAL INCLUSIONS INVOLVING RELAXED COCOERCIVE MAPPINGS IN HILBERT SPACES

  • Lee, Byung-Soo;Salahuddin, Salahuddin
    • East Asian mathematical journal
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    • v.31 no.3
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    • pp.383-391
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    • 2015
  • We considered a new system of generalized nonlinear mixed variational inclusions in Hilbert spaces and define an iterative method for finding the approximate solutions of this class of system of generalized nonlinear mixed variational inclusions. We also established that the approximate solutions obtained by our algorithm converges to the exact solutions of a new system of generalized nonlinear mixed variational inclusions.

PARAMETRIC GENERALIZED MIXED IMPLICIT QUASI-VARIATIONAL INCLUSIONS

  • Park, Jong-Yeoul;Jeong, Jae-Ug
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.889-902
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    • 2007
  • An existence theorem for a new class of parametric generalized mixed implicit quasi-variational inclusion problems is established in Hilbert spaces. Further, we study the behavior and sensitivity analysis of the solution set in this class of parametric variational inclusion problems.

SPECTRAL THEOREMS ASSOCIATED TO THE DUNKL OPERATORS

  • Mejjaoli, Hatem
    • Korean Journal of Mathematics
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    • v.24 no.4
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    • pp.693-722
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    • 2016
  • In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

PERTURBED PROXIMAL POINT ALGORITHMS FOR GENERALIZED MIXED VARIATIONAL INEQUALITIES

  • Jeong, Jae-Ug
    • East Asian mathematical journal
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    • v.18 no.1
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    • pp.95-109
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    • 2002
  • In this paper, we study a class of variational inequalities, which is called the generalized set-valued mixed variational inequality. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert spaces, we have established an existence theorem of solutions for generalized set-valued mixed variational inequalities, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized set-valued mixed variational inequalities.

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ITERATIVE ALGORITHM FOR A NEW SYSTEM OF GENERALIZED SET-VALUED QUASI-VARIATIONAL-LIKE INCLUSIONS WITH (A, ${\eta}$)-ACCRETIVE MAPPINGS IN BANACH SPACES

  • Jeong, Jae Ug
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.935-950
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    • 2012
  • In this paper, we introduce and study a new system of generalized set-valued quasi-variational-like inclusions with (A, ${\eta}$)-accretive mapping in Banach spaces. By using the resolvent operator associated with (A, ${\eta}$)-accretive mappings, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm in Banach spaces. The results presented in this paper extend and improve some known results in the literature.

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

  • Guher Gulcehre Ozbey;Guler Basak Oznur;Yelda Aygar ;Turhan Koprubasi
    • Honam Mathematical Journal
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    • v.45 no.3
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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.

A PROXIMAL POINT ALGORITHM FOR SOLVING THE GENERAL VARIATIONAL INCLUSIONS WITH M(·, ·)-MONOTONE OPERATORS IN BANACH SPACES

  • Chen, Junmin;Wang, Xian;He, Zhen
    • East Asian mathematical journal
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    • v.29 no.3
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    • pp.315-326
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    • 2013
  • 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.

A SYSTEM OF PARAMETRIC GENERALIZED NONLINEAR MIXED QUASI-VARIATIONAL INCLUSIONS IN $L_p$ SPACES

  • Jeong, Jae-Ug
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.493-506
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    • 2005
  • In this paper, we study the behavior and sensitivity analysis of the solution set for a system of parametric generalized nonlinear mixed quasi-variational inclusions in Banach spaces. By using some new and innovative technique, existence theorem for the system of parametric generalized nonlinear mixed quasi-variational inclusions in $L_p(p\ge2$ spaces is established. Our results improve the known result of Agarwal et al.[1].

ON NONLINEAR VARIATIONAL INCLUSIONS WITH ($A,{\eta}$)-MONOTONE MAPPINGS

  • Hao, Yan
    • East Asian mathematical journal
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    • v.25 no.2
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    • pp.159-169
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    • 2009
  • In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.