• Title, Summary, Keyword: variational

Search Result 998, Processing Time 0.049 seconds

REMARKS ON SOME VARIATIONAL INEQUALITIES

  • Park, Sehie
    • Bulletin of the Korean Mathematical Society
    • /
    • v.28 no.2
    • /
    • pp.163-174
    • /
    • 1991
  • This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

  • PDF

EXISTENCE AND ITERATIVE APPROXIMATIONS OF SOLUTIONS FOR STRONGLY NONLINEAR VARIATIONAL-LIKE INEQUALITIES

  • Li, Jin-Song;Sun, Ju-He;Kang, Shin-Min
    • East Asian mathematical journal
    • /
    • v.27 no.5
    • /
    • pp.585-595
    • /
    • 2011
  • In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational- like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS WITH GENERAL H-MONOTONE OPERATORS IN BANACH SPACES

  • Li, Jinsong;Wang, Wei;Cho, Min-Hyung;Kang, Shin-Min
    • East Asian mathematical journal
    • /
    • v.26 no.5
    • /
    • pp.671-680
    • /
    • 2010
  • A system of nonlinear variational inclusions involving general H-monotone operators in Banach spaces is introduced. Using the resolvent operator technique, we suggest an iterative algorithm for finding approximate solutions to the system of nonlinear variational inclusions, and establish the existence of solutions and convergence of the iterative algorithm for the system of nonlinear variational inclusions.

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

  • Lee, Byung-Soo;Salahuddin, Salahuddin
    • East Asian mathematical journal
    • /
    • v.31 no.3
    • /
    • pp.383-391
    • /
    • 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.

PROXIMAL POINTS METHODS FOR GENERALIZED IMPLICIT VARIATIONAL-LIKE INCLUSIONS IN BANACH SPACES

  • He, Xin-Feng;Lou, Jian;He, Zhen
    • East Asian mathematical journal
    • /
    • v.28 no.1
    • /
    • pp.37-47
    • /
    • 2012
  • In this paper, we study generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations in Banach spaces. It is established that generalized implicit variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish relationship between generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations. This equivalence is used to suggest a iterative algorithm for solving $J^{\eta}$-proximal operator equations.

CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF GENERALIZED VARIATIONAL INEQUALITIES

  • Jeong, Jae Ug
    • Korean Journal of Mathematics
    • /
    • v.21 no.3
    • /
    • pp.213-222
    • /
    • 2013
  • In this paper, we introduce and consider a new system of generalized variational inequalities involving five different operators. Using the sunny nonexpansive retraction technique we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.

Iterative Algorithm for a New System of Variational Inclusions with B-monotone Operators in Banach Spaces

  • Lee, Sang Keun;Jeong, Jae Ug
    • Kyungpook Mathematical Journal
    • /
    • v.53 no.3
    • /
    • pp.307-318
    • /
    • 2013
  • In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with B-monotone operator, 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 for this system of variational inclusions. The results presented in this paper extend and improve some known results in the literature.

ON THE GENERALIZED SET-VALUED MIXED VARIATIONAL INEQUALITIES

  • Zhao, Yali;Liu, Zeqing;Kang, Shin-Min
    • Communications of the Korean Mathematical Society
    • /
    • v.18 no.3
    • /
    • pp.459-468
    • /
    • 2003
  • In this paper, we introduce and study a new class of the generalized set-valued mixed variational inequalities. Using the resolvent operator technique, we construct a new iterative algorithm for solving this class of the generalized set-valued mixed variational inequalities. We prove the existence of solutions for the generalized set-valued mixed variational inequalities and the convergence of the iterative sequences generated by the algorithm.

AN ITERATIVE ALGORITHM FOR EXTENDED GENERALIZED NONLINEAR VARIATIONAL INCLUSIONS FOR RANDOM FUZZY MAPPINGS

  • Dar, A.H.;Sarfaraz, Mohd.;Ahmad, M.K.
    • Korean Journal of Mathematics
    • /
    • v.26 no.1
    • /
    • pp.129-141
    • /
    • 2018
  • In this slush pile, we introduce a new kind of variational inclusions problem stated as random extended generalized nonlinear variational inclusions for random fuzzy mappings. We construct an iterative scheme for the this variational inclusion problem and also discuss the existence of random solutions for the problem. Further, we show that the approximate solutions achieved by the generated scheme converge to the required solution of the problem.

SYMMETRIC DUALITY FOR A CLASS OF NONDIFFERENTIABLE VARIATIONAL PROBLEMS WITH INVEXITY

  • LEE, WON JUNG
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.6 no.1
    • /
    • pp.67-80
    • /
    • 2002
  • We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

  • PDF