On a Theorem by Trèves

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

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...

SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

A Note on the Descent Property Theorem for the Hybrid Conjugate Gradient Algorithm CCOMB Proposed by Andrei

In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...

Fractional dynamical systems: A fresh view on the local qualitative theorems

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...