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

Abstract. Approximation theory has been an established field of mathematics in the past century. Analysis of signals or time functions is of great importance, because it conveys information or attributes of some phenomenon. The engineers and scientists use properties of Fourier approximation for designing digital filters. In the present paper, an attempt is made to determine a theorem on the degree of approximation of a functionf , conjugate to a 2π -periodic signal belonging to the generalized weighted Lipschitz W (L r ,ξ (t)) , (r 1) -class by product (N, p n )(E,q) summability, which in turn generalizes the results of Mishra et al. [17]. In support of our theorem, we illustrated examples and deduced some corollaries from our main result of this paper.Mathematics subject classification (2010): 41A10, 42B05, 42B08, 40G05.

The purpose of this paper is to establish some coincidence, common fixed point theorems for monotone f-non decreasing self mappings satisfying certain rational type contraction in the context of a metric spaces endowed with partial order. Also, the results involving an integral type of such classes of mappings are discussed in application point of view. These results generalize and extend well known existing results in the literature. RESUMEN El propósito de este artículo es establecer teoremas de coincidencia y de punto fijo común para auto mapeos monótonos f-no decrecientes satisfaciendo ciertas contracciones de tipo racional en el contexto de espacios métricos dotados de un orden parcial. Adicionalmente, resultados que involucran clases de mapeos de tipo integral son discutidos desde un punto de vista de las aplicaciones. Estos resultados generalizan y extienden resultados bien conocidos, existentes en la literatura.

In this paper, we investigate trigonometric polynomials associated with f ∈ Lip(α, p), (0 ≤ α ≤ 1, p ≥ 1) to approximate f in L p norm to the degree of O(n −α)(0 < α ≤ 1) for a more general class of lower triangular regular matrices with non-negative entries and row sums t n .

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