Abstract. We prove comparison theorems for the H∞-calculus that allow to transfer the property of having a bounded H∞-calculus from one sectorial operator to another. The basic technical ingredient are suitable square function estimates. These comparison results provide a new approach to perturbation theorems for the H∞-calculus in a variety of situations suitable for applications. Our square f...

Fractional calculus is a branch of mathematics that studies the use fractional operators. The evolution computing allowed its application in many areas, including control theory. operators are known to well describe memory phenomena, favorable characteristic for control. Another benefit order these adds more tunable parameters controller, allowing greater flexibility and possibility improving p...

Our main purpose of this article is to study the convergence and other related properties q-Bernstein-Kantorovich operators including shifted knots real positive numbers. We design Bernstein-Kantorovich generated by basic q-calculus. More precisely, we our new in space continuous functions Lebesgue space. obtain degree with help modulus continuity integral continuity. Furthermore, establish qua...

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral, one can list out almost all of the extended densities for the pathway parameter q < 1 and q → 1. Here, we bring out the idea of thickeror thinner-tailed models as...