In this paper, we define a class R h p,m,β associated with convolution of p-valent analytic functions. Some properties in the form of coefficient inequality, growth and distortion bounds, sufficient conditions with the help of various lemmas, integral means inequality for convolution of two functions and a set of class preserving integral operators of functions belonging to this class are studi...

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types such are obtained, as (p,h) inequality and others, (p,h)-convexity is generalization As a consequence (h,m)-convexity, (s,m)-type obtained. Many consequences generalizations

we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

We study the boundary behaviour of some certain maximal implicit function. We give estimates of the maximal balls on which some implicit functions are defined and we consider some cases when the implicit function is globally defined. We extend in this way an earlier result from [3] concerning an inequality satisfied by the partial derivatives ∂h ∂x and ∂h ∂y of the map h which verifies the glob...

We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space L(H ; ν), where ν is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under bo...

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h-convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. In recent years, much attention have been given to theory of convexity beca...

4 For graphs there exists a strong connection between spectral and combinatorial 5 expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the 6 lower bound of which states that λ(G) ≤ h(G), where λ(G) is the second smallest 7 eigenvalue of the Laplacian of a graph G and h(G) is the Cheeger constant measuring 8 the edge expansion of G. We are interested in generalizat...

The continuous-and discrete-time H 1 control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems , and an LMI-based parametrization of all H 1-suboptimal controllers, including reduced-order controllers. The solvability conditions invol...

this paper undertakes the synthesis of a logic-based switching h2/h∞ state-feedback controller for continuous-time lti singular perturbation systems. our solution achieves a minimum bound on the h2 performance level, while also satisfying the h∞ performance requirements. the proposed hybrid control scheme is based on a fuzzy supervisor managing the combination of two controllers. a convex lmi-b...

We prove that the isoperimetric profile of a convex domain Ω with compact closure in a Riemannian manifold (M, g) satisfies a second order differential inequality which only depends on the dimension of the manifold and on a lower bound on the Ricci curvature of Ω. Regularity properties of the profile and topological consequences on isoperimetric regions arise naturally from this differential po...