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    On Singular Integral Operators Involving Power Nonlinearity
    (Kangwon-Kyungki Mathematical Soc, 2017) Almali, Sevgi Esen; Uysal, Gumrah; Mishra, Vishnu Narayan; Guller, Ozge Ozalp
    In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power non linearity given in the following form: T-lambda(f;x) = integral(b)(a) Sigma(n)(m=1) f(m)(t)K-lambda,K-m(x,t)dt, lambda epsilon Lambda, x epsilon (a, b), where A is an index set consisting of the non-negative real numbers, and n >= 1 is a finite natural number, at mu-generalized Lebesgue points of integrable function f epsilon L-1 (a, b). Here, f(m) denotes m - th power of the function f and (a, b) stands for arbitrary bounded interval in or I itself. We also handled the indicated problem under the assumption f epsilon L-1 (N)
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    Simultaneous Approximation for Generalized Srivastava-Gupta Operators
    (Hindawi Ltd, 2015) Acar, Tuncer; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan
    We introduce a new Stancu type generalization of Srivastava-Gupta operators to approximate integrable functions on the interval (0, infinity) and estimate the rate of convergence for functions having derivatives of bounded variation. Also we present simultenaous approximation by new operators in the end of the paper.