Any spectral function can be written as a composition of a symmetric function f : IR 7→ IR and the eigenvalue function λ(·) : S 7→ IR, often denoted by (f ◦ λ), where S is the subspace of n×n symmetric matrices. In this paper, we present some nonsmooth analysis for such spectral functions. Our main results are: (a) (f ◦ λ) is directionally differentiable if f is semidifferentiable; (b) (f ◦ λ) ...

A special class of differentiable functions on an infinite integral domain which is not a field is introduced. Some facts about these functions are established and the special case of z is studied in more detail

An inventory model is formulated with type-2 fuzzy parameters under trade credit policy and solved by using Generalized Hukuhara derivative approach. Representing demand parameter of each expert's opinion is a membership function of type-1 and thus, this membership function again becomes fuzzy. The final opinion of all experts is expressed by a type-2 fuzzy variable. For this present problem, t...

In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.

in this paper, we use the riemann-liouville fractionalintegrals to establish some new integral inequalities related tochebyshev's functional in the case of two differentiable functions.

This paper deals with the optimality conditions and dual theory of multi-objective programming problems involving generalized convexity. New classes of generalized type-I functions are introduced for arcwise connected functions, and examples are given to show the existence of these functions. By utilizing the new concepts, several sufficient optimality conditions and Mond-Weir type duality resu...

E-convex function was introduced by Youness 1 and revised by Yang 2 . Chen 3 introduced Semi-E-convex function and studied some of its properties. Syau and Lee 4 defined E-quasi-convex function, strictly E-quasi-convex function and studied some basic properties. Fulga and Preda 5 introduced the class of E-preinvex and E-prequasi-invex functions. All the above E-convex and generalized E-convex f...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...