On Approximation by Kantorovich Exponential Sampling Operators

On Bivariate Kantorovich Exponential Sampling Series

“…This provides an useful tool to approximate approximate Lebesgue integrable functions by using its samples at the nodes (e k w ) w>0 , k ∈ Z. In the spirit of improving the order of approximation for the above family, the theory of linear combination of these operators was developed in [45] using the tools of Mellin analysis. The Kantorovich type modification of sampling series has been a topic of significant applications in approximation theory over the past decades.…”

Approximation by Durrmeyer type Exponential Sampling Series

“…These operators have been studied in different settings in [12,20,21,4]. In order to reduce the time-jitter error, the Kantorovich modification of these operators has been introduced and studied in [38,45]. The time-jitter error causes when the sample values can not be obtained exactly at the nodes.…”

“…where f : R + → R is locally integrable such that the above series is convergent for every x ∈ R + . In view of Theorem 3.1 in [45], it is apparent that the Kantorovich exponential sampling operators (1.1) fails to improve the order of approximation in the asymptotic formula. This motivates us to adopt another approach, known as Durrmeyer method, where the integral mean is replaced by a general convolution operator.…”

“…In Section 4, we establish the basic convergence theorem and asymptotic formula for the proposed family operators (3.2). Using Peetre's K functional [3,45], we obtain the quantitative estimates of the Voronovskaya type theorem. Section 5 is devoted to the study of suitable linear combinations of the family of operators (3.2) which produce the better order of approximation.…”

“…Section 5 is devoted to the study of suitable linear combinations of the family of operators (3.2) which produce the better order of approximation. The idea of considering the linear combinations of the operators is a prominent method to improve the order of convergence, see [10,11,4,14,15,45]. In last section, we discuss few examples of the well known kernels along with the graphical representations.…”