Differential sandwich theorem for certain class of analytic functions associated with an integral operator

In this paper we obtain some applications of first order differential subordination and superordination result involving an integral operator for certain normalized analytic function.

The subnormal structure of classical-like groups over commutative rings

Let 𝑛 be an integer greater than or equal to 3, and let (R,\Delta) be a Hermitian form ring, where 𝑅 is commutative. We prove that if 𝐻 is a subgroup of the odd-dimensional unitary group \operatorname{U}_{2n+1}(R,\Delta) normalised by a relative elementary subgroup \operatorname{EU}_{2n+1}((R,\Delta),(I,\Omega)), then there is an odd form ideal (J,\Sigma) such that\operatorname{EU}_{2n+1}((R,\Delta),(JI^{k},\Omega_{\mathrm{min}}^{JI^{k}}\dotplus\Sigma\circ I^{k}))\leq H\leq\operatorname{CU}_{2n+1}((R,\Delta),(J,\Sigma)),where k=12 if n=3 respectively k=10 if n\geq 4. As a consequence of this result, we obtain a sandwich theorem for subnormal subgroups of odd-dimensional unitary groups.

Spectrum of Signless 1-Laplacian on Simplicial Complexes

We introduce the signless 1-Laplacian and the dual Cheeger constant on simplicial complexes. The connection of its spectrum to the combinatorial properties like independence number, chromatic number and dual Cheeger constant is investigated. Our estimates can be comparable to Hoffman's bounds on Laplacian eigenvalues of simplicial complexes. An interesting inequality involving multiplicity of the largest eigenvalue, independence number and chromatic number is provided, which could be regarded as a variant version of Lovász sandwich theorem. Also, the behavior of 1-Laplacian under the topological operations of wedge and duplication of motifs is studied. The Courant nodal domain theorem in spectral theory is extended to the setting of signless 1-Laplacian on complexes.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

Sandwich theorem for reciprocally strongly convex functions

We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

A Generalization of m-Convexity and a Sandwich Theorem

Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.