On a generalization of uniformly convex and related functions

AbstractIn this paper, we define and study some subclasses of analytic functions by using the concept of k-uniformly convexity. Several interesting properties, coefficients and radius problems are investigated. The behaviour of these classes under a certain integral operator is also studied. We indicate the relevant connections of our results with various known ones

New classes of higher order variational-like inequalities

In this paper, we prove that the optimality conditions of the higher order convex functions are characterized by a class of variational inequalities, which is called the higher order variational inequality. Auxiliary principle technique is used to suggest an implicit method for solving higher order variational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results

Harmonic Variational Inequalities

In this paper, we consider a new class of variational inequalities, which is called the harmonic variational inequality. It is shown that that the minimum of a differentiable harmonic convex function on the harmonic convex set can be characterized by the harmonic variational inequality. We use the auxiliary principle technique to discuss the existence of a solution of the harmonic variational inequality. Results proved in this paper may stimulate further research in this field

On sensitivity analysis of general variational inequalities

It is well known that the Wiener-Hopf equations are equivalent to the general variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the general variational inequalities without assuming the differentiability of the given data. Since the general variational inequalities include classical variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. In fact, our results can be considered as a significant extension of previously known results

Proximal Point Methods for Solving Mixed Variational Inequalities on the Hadamard Manifolds

We use the auxiliary principle technique to suggest and analyze a proximal point method for solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered. Results can be viewed as refinement and improvement of previously known results

New classes of exponentially general nonconvex variational inequalities

In this paper, some new classes of exponentially general nonconvex variational inequalities are introduced and investigated. Several special cases are discussed as applications of these nonconvex variational inequalities. Projection technique is used to establish the equivalence between the non covex variational inequalities and fixed point problem. This equivalent formulation is used to discuss the existence of the solution. Several inertial type methods are suggested and analyzed for solving exponentially general nonconvex variational inequalities. using the technique of the projection operator and dynamical systems. Convergence analysis of the iterative methods is analyzed under suitable and appropriate weak conditions. In this sense, our result can be viewed as improvement and refinement of the previously known results. Our methods of proof are very simple as compared with other techniques

SOME PROPERTIES OF EXPONENTIALLY PREINVEX FUNCTIONS

In this paper, we introduce some new concepts of the exponentially preinvex functions. We investigate several properties of the exponentially preinvex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational-like inequalities. Several interesting results characterizing the exponentially preinvex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results

Existence Results for General Mixed Quasivariational Inequalities

We consider and study a new class of variational inequality, which is called the general mixed quasivariational inequality. We use the auxiliary principle technique to study the existence of a solution of the general mixed quasivariational inequality. Several special cases are also discussed. Results proved in this paper may stimulate further research in this area

Radius problems for a subclass of close-to-convex univalent functions

Let P[A,B], −1≤Bβ, 0≤β<1 and z∈E. The functions in this class are close-to-convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved