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In the present paper, we obtain some new results by applying well-known Jack?s lemma. Moreover, the second-order differential subordinations associated with convex functions are also considered.

In the present work, a sharp bound on the modulus of the initial coefficients for powers of strongly Bazilević functions is obtained. As an application of these results, certain conditions are investigated under which the Littlewood-Paley conjecture holds for strongly Bazilević functions for large values of the parameters involved therein. Further, sharp estimate on the generalized Fekete-Szeg&ouml, functional is also derived. Relevant connections of our results with the existing ones are also made.

We investigate several sufficient conditions on a function to be convex in one direction or starlike in one direction.

The object of the present paper is to give some applications of the first-order differential subordinations. We also extend and improve several previously known results.

An efficient and facile one-pot synthesis is described for the preparation of novel 2-amino-5-hydroxy-4H-chromene derivatives with a spirooxindole nucleus using Ca(OH)2-mediated three-component reactions of substituted resorcinols with isatins and malononitrile. This simple method provided a variety of biologically interesting diverse 2-amino-5-hydroxy-4H-chromene derivatives in moderate yields under mild reaction conditions.

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sampled-data representation of a non-affine nonlinear system with constant input time-delay. The mathematical expressions of the discretization scheme are presented and the ability of the algorithm is tested for some of the examples. The proposed scheme provides a finite-dimensional representation for nonlinear systems with time-delay enabling existing controller design techniques to be applied to them. For all the case studies, various sampling rates and time-delay values are considered.

This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.

An efficient and facile one-pot synthesis is described for the preparation of novel 2-amino-5-hydroxy-4H-chromene derivatives with a spirooxindole nucleus using Ca(OH)2-mediated three-component reactions of substituted resorcinols with isatins and malononitrile. This simple method provided a variety of biologically interesting diverse 2-amino-5-hydroxy-4H-chromene derivatives in moderate yields under mild reaction conditions.