Generalised multivalued inequalities are studied in this paper. Our results enable us to discuss control problems and differential inclusions on proximate retracts.

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...

Gender-based inequalities in health have been frequently documented. This paper examines the extent to which these inequalities reflect the different social experiences and conditions of men's and women's lives. We address four specific questions. Are there gender differences in mental and physical health? What is the relative importance of the structural, behavioural and psychosocial determina...

A new class of analytic functions of complex order is defined using a generalized differential operator. Coefficient inequalities, sufficient condition and an interesting subordination result are obtained.

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...

We derive differential inequalities and difference inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian, Rσ(z) := ∑ k (z − λk) σ +. Here {λk} ∞ k=1 are the ordered eigenvalues of the Laplacian on a bounded domain Ω ⊂ Rd, and x+ := max(0, x) denotes the positive part of the quantity x. As corollaries of these inequalities, we derive Weyl-type bounds on λk, on averages such as λ...

We present a general numerical method for computing guaranteed two-sided bounds for principal eigenvalues of symmetric linear elliptic differential operators. The approach is based on the Galerkin method, on the method of a priori–a posteriori inequalities, and on a complementarity technique. The two-sided bounds are formulated in a general Hilbert space setting and as a byproduct we prove an a...

Abstract Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays main study existence uniqueness initial boundary value problems for differential equations. this work, we prove some new Jensen-type inequalities m -convex functions apply them to generalized Riemann-Liouville-type integral operators. Furth...