Suchergebnisse

In this paper, by using Hölder-İşcan, Hölder integral inequality and a general identity for differentiable functions we can get new estimates on generalization of Hadamard, Ostrowski and Simpson type integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained Hölder-İşcan integral inequality is better than the result obtained Hölder inequality.
Keywords: Hölder-İşcan scan inequality, Hermite-Hadamard inequality, Simpson and Ostrowski type inequality, midpoint and trapezoid type inequality, quasi-convex functions.

AbstractIt is shown that a lsc function is convex if and only if the minimal set of any linear perturbation of the function is convex. That fact also yields that the convexity of a function is equivalent to the quasiconvexity of its all linear perturbations.

Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions, i.e., for functions $f:X\to\R$ that satisfy the inequality $f(x\circ y)\leq pf(x)+qf(y)$, where $\circ$ is a binary operation on $X$ and $p,q$ are positive constants. As an application, we also obtain an extension of the Karush--Kuhn--Tucker theorem for this class of functions.

AbstractThe purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

The objective of this paper is to present some geometric properties of the close to convex function f when f is an analytic, univalent self-conformal mapping defined in the open unit disk D={z∈C: |z|<1}, and on the boundary of D. One of the goals of this work was determining the sharp bound for the function of form f(z)=z/(1-z)^2δ , 0<δ<1, when R(f^'/g^' (w_1))≥-2+δ/w_1 , for a some w_1∈∂D And another, if f has angular limit at p∈∂D . Then the inequality |(f^' (z))/(g^' (z) )|≥(-(1-2δ))/2(1+ δ) is sharp with extremal functions f(z)=z/(1-z)^2δ , and g(z)=z/(1+z), where 0<δ<1. Finally, if f is extended continuously to the boundary of D , then | (f^'/g^' )(p)|≥ |1-2δ|(|1-2δ|-2)/|p-δ | ; 0<δ<1.

de la Sen, manuel/0000-0001-9320-9433 ; WOS: 000484158700003 ; In this paper, we consider classes of harmonic convex functions and give their special characterizations. Furthermore, we consider Hermite Hadamard type inequalities related to these classes to give some non-numeric estimates of well-known definite integrals. ; Basque GovernmentBasque Government [IT1207/19] ; The authors are grateful to the Basque Government by its support through Grant IT1207/19. This research article is partially supported by Higher Education Commission of Pakistan too.

AbstractIn this article an algorithm for computing upper and lower ϵ approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ϵ the number of iterations is bounded by magnified image, where D is the total increase in slope of h. As an application we discuss separable convex programs.

In this paper, we are introducing very first time the class of ψ − (α, β, γ, δ)−convex function in mixed kind, which is the generalization of many classes of convex functions. We would like to state well-known Ostrowski inequality via Montgomery identity for ψ−(α, β, γ, δ)−convex function in mixed kind. In addition, we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are ψ − (α, β, γ, δ)-convex functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.
Keywords: Ostrowski inequality, Montgomery identity, convex functions, special means.