• Title/Summary/Keyword: mixed Lipschitz continuous

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ERROR BOUNDS FOR NONLINEAR MIXED VARIATIONAL-HEMIVARIATIONAL INEQUALITY PROBLEMS

  • A. A. H. Ahmadini;Salahuddin;J. K. Kim
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.1
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    • pp.15-33
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    • 2024
  • In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

DEGREE OF APPROXIMATION FOR BIVARIATE SZASZ-KANTOROVICH TYPE BASED ON BRENKE TYPE POLYNOMIALS

  • Begen, Selin;Ilarslan, H. Gul Ince
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.251-268
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    • 2020
  • In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szász-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szász-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bögel continuous functions.

STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR A CLASS OF NONLINEAR SET-VALUED VARIATIONAL INCLUSIONS

  • Ding, Xie Ping;Salahuddin, Salahuddin
    • Korean Journal of Mathematics
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    • v.25 no.1
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    • pp.19-35
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    • 2017
  • In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

SENSITIVITY ANALYSIS FOR SYSTEM OF PARAMETRIC GENERALIZED QUASI-VARIATIONAL INCLUSIONS INVOLVING R-ACCRETIVE MAPPINGS

  • Kazmi, Kaleem Raza;Khan, Faizan Ahmad;Ahmad, Naeem
    • Journal of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1319-1338
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    • 2009
  • In this paper, using proximal-point mappings technique of Raccretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to parameters. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [3, 23, 24, 32, 33, 34].

Some Approximation Results by Bivariate Bernstein-Kantorovich Type Operators on a Triangular Domain

  • Aslan, Resat;Izgi, Aydin
    • Kyungpook Mathematical Journal
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    • v.62 no.3
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    • pp.467-484
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    • 2022
  • In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.