INTEGRAL INEQUALITIES FOR HARMONICALLY s-GODUNOVA-LEVIN FUNCTIONS

In this paper, some new classes of harmonically convex functions areintroduced and investigated. We derive several Hermite-Hadamard inequalities forthese new classes of harmonically convex functions. The ideas and techniques of thispaper may be extended for other classes of convex functions

Quasi Variational Inclusions Involving Three Operators

In this paper, we consider some new classes of the quasi-variational inclusions involving three monotone operators. Some interesting problems such as variational inclusions involving sum of two monotone operators, difference of two monotone operators, system of absolute value equations, hemivariational inequalities and variational inequalities are the special cases of quasi variational inequalities. It is shown that quasi-variational inclusions are equivalent to the implicit fixed point problems. Some new iterative methods for solving quasi-variational inclusions and related optimization problems are suggested by using resolvent methods, resolvent equations and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under monotonicity. Some special cases are discussed as applications of the main results

Quasi Variational Inclusions Involving Three Operators

In this paper, we consider some new classes of the quasi-variational inclusions involving three monotone operators. Some interesting problems such as variational inclusions involving sum of two monotone operators, difference of two monotone operators, system of absolute value equations, hemivariational inequalities and variational inequalities are the special cases of quasi variational inequalities. It is shown that quasi-variational inclusions are equivalent to the implicit fixed point problems. Some new iterative methods for solving quasi-variational inclusions and related optimization problems are suggested by using resolvent methods, resolvent equations and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under monotonicity. Some special cases are discussed as applications of the main results

Some new estimates of Hermite-Hadamard inequalities via harmonically r-convex functions

In this paper, we introduce the class of harmonically r-convex functions. We derive some Hermite-Hadamard type inequalities for this class of convex functions

Simpson type inequalities and applications

A new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of \sigma >0. We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula

SOME NEW Q-ESTIMATES FOR CERTAIN INTEGRAL INEQUALITIES

In this paper, we consider a newly introduced class of convex functions that is eta-convex functions. We give some new quantum analogues for Hermite-Hadamard, Iynger and Ostrowski type inequalities via eta-convex functions. Some special cases are also discussed

FRACTIONAL OSTROWSKI INEQUALITIES FOR (s,m)(s,m)-GODUNOVA-LEVIN FUNCTIONS

In this paper, we introduce some new classes of s-Godunova-Levin functions, which are called as sm-Godunova-Levin functions of first and second kinds. We show that these classes contains some previouslyknown classes of convex functions. Finally we establish some new Ostrowski inequalities for sm-Godunova-Levin functions via fractional integrals. Some special cases are also discussed

FAMILY ACANTHACEAE AND GENUS APHELANDRA: ETHNOPHARMACOLOGICAL AND PHYTOCHEMICAL REVIEW

Aphelandra belong to family Acanthaceae. We have reviewed traditional uses, pharmacological potential and phytochemical study of family Acanthaceae and genus Aphelandra. Traditionally the most important part use in Acanthaceae is the leaves and they are used externally for wounds. We have found that Acanthaceae possess antifungal, cytotoxic, anti-inflammatory, anti-pyretic, anti-oxidant, insecticidal, hepatoprotective, immunomodulatory, Anti- platelet aggregation and anti-viral potential. Phytochemical reports on family Acanthaceae are glycosides, flavonoids, benzonoids, phenolic compounds, naphthoquinone and triterpenoids. We have also document genus Aphelandra, its phytochemical and pharmacological potential