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Approximation properties of certain summation integral type operators

100%

Patel P. , Mishra V. N.

Demonstratio Mathematica

2015

tom Vol. 48, nr 1

77--90

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

Strong Cesáro summability of triple Fourier integrals

80%

Mishra V. N. , Khatri K. , Mishra L. N.

Fasciculi Mathematici

2014

tom Nr 53

95--112

The theory of summability is a very extensive field, which has various applications. We prove the following theorem. Assume ƒ ϵ L∞(R3) with bounded support. If ƒ is continuous at some point (x1, x2, X3) ϵ R3, then the triple Fourier integral of ƒ is strongly q-Casáro summable at (x1, x2, X3) to the function value ƒ (x1, x2, X3) for every 0 < q < ∞. Furthermore, if ƒ is continuous on some open subset G of R3, then the strong q-Cesáro summability of the triple Fourier integral of ƒ is locally uniform on G.

Composite relaxed resolvent operator and Yosida approximation operator for solving a system of Yosida inclusions

80%

Ahmad R. , Mishra V. N. , Ishtyak M. , Rahaman M.

tom Vol. 24, nr 2

185--195

In this paper, we first study a composite relaxed resolvent operator and prove some of its properties. After that, we introduce a Yosida approximation operator based on the composite relaxed resolvent operator and demonstrate some properties of the Yosida approximation operator. Finally, we obtain the solution of a system of Yosida inclusions by applying these concepts.We construct a conjoin example in support of many concepts derived in this paper. Our concepts and results are new in the literature and can be used for further research.