Lakshmi Narayan Mishra

Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators

In the present paper, we study an inverse result in simultaneous approximation for Baskakov-Durrmeyer-Stancu type operators.MSC:41A25, 41A35, 41A36.

Statistical approximation by Kantorovich-type discrete q-Beta operators

The aim of the present paper is to introduce a Kantorovich-type modification ofthe q-discrete beta operators and to investigate their statistical andweighted statistical approximation properties. Rates of statistical convergenceby means of the modulus of continuity and the Lipschitz-type function are alsoestablished for operators. Finally, we construct a bivariate generalization ofthe operator and also obtain the statistical approximation properties.MSC: 41A25, 41A36.

Some Approximation Properties of -Baskakov-Beta-Stancu Type Operators

This paper deals with new type -Baskakov-Beta-Stancu operators defined in the paper. First, we have used the properties of -integral to establish the moments of these operators. We also obtain some approximation properties and asymptotic formulae for these operators. In the end we have also presented better error estimations for the -operators.

On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(Lr, ξ(t))(r ⩾ 1)-class by matrix (C1 ⋅ Np) operator of conjugate series of its Fourier series

Abstract In the present paper, a new theorem on the degree of approximation of function f ∼ , conjugate to a 2 π periodic function f belonging to the generalized weighted Lipschitz W ( L r , ξ ( t ) ) ( r ⩾ 1 ) -class by dropping the monotonicity condition on the generating sequence { p n } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22].

Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces

We establish some unique fixed point theorems in complete partial metric spaces for generalized weakly -contractive mappings, containing two altering distance functions under certain assumptions. Also, we discuss some examples in support of our main results.

Product Summability Transform of Conjugate Series of Fourier Series

A known theorem, Nigam (2010) dealing with the degree of approximation of conjugate of a signal belonging to Lip𝜉(𝑡)-class by (𝐸,1)(𝐶,1) product summability means of conjugate series of Fourier series has been generalized for the weighted 𝑊(𝐿𝑟,𝜉(𝑡)), (𝑟≥1),(𝑡>0)-class, where 𝜉(𝑡) is nonnegative and increasing function of 𝑡, by 𝐸1𝑛𝐶1𝑛 which is in more general form of Theorem 2 of Nigam and Sharma (2011).

On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order

In this paper, we present some results on existence of solutions for a quadratic Volterra integral equation of fractional order in two independent variables. This equation is considered in the Banach space of real functions, defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive. An example is provided to illustrate the theory.

Simultaneous Approximation for Generalized Srivastava-Gupta Operators

We introduce a new Stancu type generalization of Srivastava-Gupta operators to approximate integrable functions on the interval 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.

Trigonometric approximation of functions belonging to Lipschitz class by matrix ( C 1 ⋅ N p ) operator of conjugate series of Fourier series

In the present paper, a new theorem on the degree of approximation of a function f˜, conjugate to a 2π periodic function f belonging to the Lipα (0<α≤1) class without the monotonicity condition on the generating sequence {pn} has been established, which in turn generalizes the results of Lal (Appl. Math. Comput. 209: 346-350, 2009) on a Fourier series.MSC:40G05, 41A10, 42B05, 42B08.

On trigonometric approximation of W ( L p , ξ ( t ) ) (p ≥ 1 ) function by product ( C , 1 ) ( E , 1 ) means of its Fourier series

In the present paper, we generalize a theorem of Lal and Singh (Indian J. Pure Appl. Math. 33(9):1443-1449, 2002) on the degree of approximation of a function belonging to the weighted W(Lp,ξ(t)) (p≥1)-class using product (C,1)(E,1) means of its Fourier series. We have used here the modified definition of the weighted W(Lp,ξ(t)) (p≥1)-class of functions in view of Khan (Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 31:123-127, 1982) and rectified some errors appearing in the paper of Lal and Singh (Indian J. Pure Appl. Math. 33(9):1443-1449, 2002). A few applications of approximation of functions will also be highlighted.MSC: 40C99, 40G99, 41A10, 42B05, 42B08.