Browsing by Author "Mohapatra, R.N."

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    Hyers–Ulam stability of unbounded closable operators in Hilbert spaces
    (John Wiley and Sons Inc, 2024) Majumdar, A.; Johnson, P.S.; Mohapatra, R.N.
    In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of (Formula presented.) block matrix (Formula presented.) in order to have the Hyers–Ulam stability. © 2024 Wiley-VCH GmbH.
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    Local convergence of a uniparametric halley-type method in banach space free of second derivative
    (2015) Argyros, I.K.; George, S.; Mohapatra, R.N.
    We present a local convergence analysis of a uniparametric Halley-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fr chet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fr chet-derivative [26]. Numerical examples are also provided in this study.
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    Local convergence of a uniparametric halley-type method in banach space free of second derivative
    (International Publications internationalpubls@yahoo.com, 2015) Argyros, I.K.; George, S.; Mohapatra, R.N.
    We present a local convergence analysis of a uniparametric Halley-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative [26]. Numerical examples are also provided in this study.
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    MULTIPLIERS FOR OPERATOR-VALUED BESSEL SEQUENCES AND GENERALIZED HILBERT-SCHMIDT CLASSES
    (Korean Society for Computational and Applied Mathematics, 2022) Mahesh Krishna, K.M.; Johnson, P.S.; Mohapatra, R.N.
    In 1960, Schatten studied operators of the form Σ∞ n=1 λn(xn⊗yn), where {xn}n and {yn}n are orthonormal sequences in a Hilbert space, and {λn}n ∈ ℓ∞(ℕ). Balazs generalized some of the results of Schatten in 2007. In this paper, we further generalize results of Balazs by studying the operators of the form Σ∞ n=1 λn(A∗ nxn ⊗ B∗ n yn), where {An}n and {Bn}n are operator-valued Bessel sequences, {xn}n and {yn}n are sequences in the Hilbert space such that {∥xn∥∥yn∥}n ∈ ℓ∞(ℕ). We also generalize the class of Hilbert-Schmidt operators studied by Balazs. © 2022 KSCAM.