Free Cells in Hyperspaces of Graphs

Often for understanding a structure, other closely related structures with the former are associated. An example of this is the study of hyperspaces. In this paper, we give necessary and sufficient conditions for the existence of finitely-dimensional maximal free cells in the hyperspace C(G) of a dendrite G; then, we give necessary and sufficient conditions so that the aforementioned result can be applied when G is a dendroid. Furthermore, we prove that the arc is the unique arcwise connected, compact, and metric space X for which the anchored hyperspace Cp(X) is an arc for some p∈X.

Multiobjective fractional programming problems and the sufficient condition involving Hb – (p, r)-η- invex function

On the basis of arcwise connected convex functions and (p, r) −η - invex functions, we established Hb –(p, r) –η- invex functions. Based on the generalized invex assumption of new functions, the solutions of a class of multiobjective fractional programming problems are studied, and the sufficient optimality condition for the feasible solutions of multiobjective fractional programming problems to be efficient solutions are established and proved.

Periodic points for amenable group actions on uniquely arcwise connected continua

We show that any action of a countable amenable group on a uniquely arcwise connected continuum has a periodic point of order $\leq 2$ .

Further results on the arcwise connectedness of solution sets of discontinuous quantum stochastic differential inclusions

In the framework of the Hudson–Parthasarathy quantum stochastic calculus, we employ a recent generalization of the Michael selection results in the present noncommutative settings to prove that the function space of the matrix elements of solutions to discontinuous quantum stochastic differential inclusion (DQSDI) is arcwise connected.