Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.     

Multiobjective programming problems with (G,C,ρ)-convexity

In this paper, we deal with multiobjective programming problems involving functions which are not necessarily differential. A new concept of generalized convexity, which is called (G,C,??)-convexity, is introduced. We establish not only sufficient but also necessary optimality conditions for multiobjective programming problems from a viewpoint of the new generalized convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.     

Second order duality for nondifferentiable multiobjective programming problem involving (F, α, ρ, d)-V-type I functions

In this paper, new classes of second order (F, α, ρ, d)-V-type I functions for a nondifferentiable multiobjective programming problem are introduced. Furthermore, second order Mangasarian type and general Mond-Weir type duals problems are formulated for a nondifferentiable multiobjective programming problem. Weak strong and strict converse duality theorems are studied in both cases assuming the involved functions to be second order (F, α, ρ, d)-V-type I.     

Generalized multiobjective symmetric duality under second-order (F, α, ρ, d)-convexity

In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f : Rn × Rm → Rk and g : Rn × Rm → Rl in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order(F, α, ρ, d)-convexity assumptions. A nontrivial example which is second-order(F, α, ρ, d)-convex but not secondorder convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order(F, α, ρ, d)-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.     

On a nonlocal problem for a fourth-order parabolic equation with the fractional Dzhrbashyan–Nersesyan operator

We study a nonlocal problem for a fractional partial differential equation with the Dzhrbashyan–Nersesyan fractional differentiation operator. By separation of variables, we prove a theorem on the existence and uniqueness of a regular solution of this problem.     

On a boundary value problem for an equation of mixed type with a Riemann–Liouville fractional partial derivative

For an equation of mixed type with a Riemann–Liouville fractional partial derivative, we prove the uniqueness and existence of a solution of a nonlocal problem whose boundary condition contains a linear combination of generalized fractional integro-differentiation operators with the Gauss hypergeometric function in the kernel. A closed-form solution of the problem is presented.     

On Tanaka formulae for (α,d,β)-superprocesses

In this paper,Tanaka formulae for (α,d,β)-superprocesses in the dimensions where the local time exists are established under the optimal initial condition.     

Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR - In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality...     

Sufficient Conditions and Duality for a Class of Multiobjective Fractional Programming Problems with Higher-Order (F,α,ρ,d)-Convexity

In this paper, a class of multiobjective fractional programming problems (denoted by (MFP)) is considered. First, the concept of higher-order (F,α,ρ,d)-convexity of a function f:C→R with respect to the differentiable function φ:R ⁿ ×R ⁿ →R is introduced, where C is an open convex set in R ⁿ and α:C×C→R ₊?{0} is a positive value function. And an important property, which the ratio of higher-order (F,α,ρ,d)-convex functions is also higher-order (F,α ^′,ρ ^′,d ^′)-convex, is proved. Under the higher-order (F,α,ρ,d)-convexity assumptions, an alternative theorem is also given. Then, some sufficient conditions characterizing properly (or weakly) efficient solutions of (MFP) are obtained from the above property and alternative theorem. Finally, a class of dual problems is formulated and appropriate duality theorems are proved.     

On the behaviour ast→∞ of solutions of the second mixed problem for a second-order parabolic equation

In this paper is distinguished a geometric characteristic of the unbounded domain , that determines the rate of stabilization fort of the solution in (t>0)× of the second boundary value problem for a second-order parabolic equation, in which the initial function decreases sufficiently rapidly as |x|.     

Multiobjective fractional programming problems involving (p,r)?ρ?(η,θ)-invex function

In this paper we move forward in the study of multiobjective fractional programming problem and established sufficient optimality conditions under the assumption of (p,r)????(??,??)-invexity. Weak, strong and strict converse duality theorems are also derived for three type of dual models related to multiobjective fractional programming problem involving aforesaid invex function.     

Representing systems for the space of holomorphic functions in a (ρ,α)-convex domain

This article is a natural supplement to Chapter 5 ofAsymptotic Characteristics of Entire Functions and Their Applications [Nauka, Novosibirsk (1991)]. Earlier, for the functions holomorphic in the closure of a (ρ,α)-convex bounded domain D, the author found a criterion of the existence of a series expansion in a special system of entire functions. Here it is shown that the same criterion applies to the functions holomorphic in D. Moreover, a new integral representation of entire functions is described, which enables one to construct new representing systems for the spaces of holomorphic functions and H(D). Bibliography: 17 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993, pp. 91–196. Translated by D. V. Yakubowich.     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

Generalized Taylor series for the class of functions H(ρ,m)

The nonquasianalytic class of functions H(, m) is constructively described by generalized Taylor series. Nonredundant discrete information in this connection is given with the help of first and second differences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 1007–1009, July, 1990.     

On (α,β)-Metrics with Reversible Geodesics

In this paper,we get necessary and sufficient conditions for a Finsler space endowed with an(α,β)-metric where its geodesic coefficients G~i(x,y) and the reverse of geodesic coefficients G~i(x,-y) have the same Douglas curvature.They are the conditions such that(α,β)-metrics have reversible geodesics.