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

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 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

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

Some Characterizations of General Preinvex Functions

In this paper, we consider a new class of general preinvex functions involving an arbitrary function. We show that the optimality condition for general preinvex functions on general invex set can be characterized by a class of variational-like inequality. We also derive some integral inequalities of Hermite-Hadamard type via general preinvex functions. Some special cases are also discussed. Our results represent a significant refinement of the previously known results. These results may stimulate further research in this area

Unified inequalities of the q-Trapezium-Jensen-Mercer type that incorporate majorization theory with applications

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of ${\mathfrak{q}}$-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the $_{{\varsigma_{1}}}{\mathfrak{q}}$ and $^{{{\varsigma_{2}}}}{\mathfrak{q}}$ differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint ${\mathfrak{q}}$-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations