Applications of q-Calculus in Operator Theory

By Ali Aral, Vijay Gupta, Ravi P. Agarwal. 2013

532 citations recorded by the source corpus.

Subfields: Information Systems, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1ba3300124bad7fda14af65a8fe304dc02a467e8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Information Systems

Tuncer Acar

In Statistics and Probability

Citations in the corpus

Some Subordination Results on -Analogue of Ruscheweyh Differential Operator (2014, background): “A comprehensive study on applications of q-analysis in operator theory may be found in [12].”
Convolution Properties for Certain Classes of Analytic Functions Defined by -Derivative Operator (2014, background): “A comprehensive study on applications of q-calculus in operator theory may be found in [12].”
(p, q)-Beta functions and applications in approximation (2016, background): “Introduction In the last decade, the generalizations of several operators to quantum variant have been introduced and their approximation behavior have been discussed [see for instance [1], [5], [8], [12], [10] etc].”
Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization (2017, background): “Definition 7 (see [21] and [22]) For 0 < jqj < 1, the q-derivative operator Dq is defined by Dqf .”
On Pointwise Convergence of q-Bernstein Operators and Their q-Derivatives (2015, result): “We refer some of these studies as [2, 3] and references therein.”
Rate of Approximation by Finite Iterates of $$q$$q-Durrmeyer Operators (2016, background): “[1] and the classical monograph by Kac and Cheung [2].”
(p,q)‐Generalization of Szász–Mirakyan operators (2015, background): “KYAN OPERATORS 9´ 5. Weighted Approximation BySn,p,q Now we give approximation properties of the operators Sn,p,q on the interval [0,∞). Since Sn,p,q 1+t2;x = 1+pqx2 + q2x [n]p,q ≤ 1+x2 +x and if x ∈ [0,1], then x ≤ 1 and if x ∈ (1,∞), then x ≤ x2. Hence we have Sn,p,q 1+t2;x ≤ 2 1+x2 whichsaysthat ”
Coefficient estimates of new classes of q-starlike and q-convex functions of complex order (2016, unknown): “A comprehensive study on applications of q calculus in operator theory may be found in [11].”