On Smarandache's Podaire Theorem

On Smarandache's form of the individual Fermat-Euler theorem

In the paper it is shown how a form of the classical FERMAT-EULER Theorem discovered by F • SMARANDA CHE fits into the generalizations found by S.SCHWARZ, M.LASSAK and the author. Then we show how SMARANDACHE'S algorithm can be used to effective computations of the so called group membership. AMS Subject Classification (1991): 11A07, llR04, 11T99, 11YI6, 13F05

Some inequalities concerning Smarandache's function

The objectives of this article are to study the sum IS(d) and to find some upper din bounds for Smarandache's function. This sum is proved to satisfy the inequality IS(d) ~ n at most all the composite numbers, Using this inequality, some new din upper bounds for Smarandache's function are found. These bounds improve the well-known inequality Sen) ~ n.

Computational Aspect of Smarandache's Function

The note presents an algorithm for the Smarandache's function computation. The complexity of algorithm is studied using the main properties of function. An interesting inequality is found giving the complexity of thefunction on the set {1.2 •...• n}.

On Some of the Smarandache's Problems

On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...