• Title/Summary/Keyword: Lipschitz-type class

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ON A SEQUENCE OF KANTOROVICH TYPE OPERATORS VIA RIEMANN TYPE q-INTEGRAL

  • Bascanbaz-Tunca, Gulen;Erencin, Aysegul;Tasdelen, Fatma
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.303-315
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    • 2014
  • In this work, we construct Kantorovich type generalization of a class of linear positive operators via Riemann type q-integral. We obtain estimations for the rate of convergence by means of modulus of continuity and the elements of Lipschitz class and also investigate weighted approximation properties.

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.

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.

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.

MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

  • Lee Byung-Soo
    • The Pure and Applied Mathematics
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    • v.13 no.3 s.33
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    • pp.197-206
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    • 2006
  • This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

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ON APPROXIMATION PROPERTIES OF STANCU VARIANT λ-SZÁSZ-MIRAKJAN-DURRMEYER OPERATORS

  • Aslan, Resat;Rathour, Laxmi
    • Korean Journal of Mathematics
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    • v.30 no.3
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    • pp.539-553
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    • 2022
  • In the present paper, we aim to obtain several approximation properties of Stancu form Szász-Mirakjan-Durrmeyer operators based on Bézier basis functions with shape parameter λ ∈ [-1, 1]. We estimate some auxiliary results such as moments and central moments. Then, we obtain the order of convergence in terms of the Lipschitz-type class functions and Peetre's K-functional. Further, we prove weighted approximation theorem and also Voronovskaya-type asymptotic theorem. Finally, to see the accuracy and effectiveness of discussed operators, we present comparison of the convergence of constructed operators to certain functions with some graphical illustrations under certain parameters.

ON KANTOROVICH FORM OF GENERALIZED SZÁSZ-TYPE OPERATORS USING CHARLIER POLYNOMIALS

  • Wafi, Abdul;Rao, Nadeem;Deepmala, Deepmala
    • Korean Journal of Mathematics
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    • v.25 no.1
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    • pp.99-116
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    • 2017
  • The aim of this article is to introduce a new form of Kantorovich $Sz{\acute{a}}sz$-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

GENERALIZED NONLINEAR MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

  • Lee, Byung-Soo;Khan M. Firdosh;Salahuddin Salahuddin
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.689-700
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    • 2006
  • In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.