On Contractibility of the Operator i-t Nabla f
On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
On convergence for the -integral
On convergence of Börsch-Supan's method with Weierstrass' corrections.
On convergence of -series involving basic hypergeometric series.
On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces.
On convex and *-concave multifunctions
A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion holds for every s,t ∈ [a,b], s < t.
On convex functions bounded below.
On convex functions bounded below. (Short Communication).
On convex stochastic processes.
On convolution of continuous functions
On co-ordinated quasi-convex functions
A function , where is an interval, is said to be a convex function on if holds for all and . There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensen-convex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex functions...
On -preinvex-type functions.
On Darboux selections
On Darboux solutions of the Euler's equation.
On decomposing the plane into connected or one-to-one curves
On Denjoy property and on approximate partial derivatives
On Denjoy type extensions of the Pettis integral
In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
On Denjoy-Dunford and Denjoy-Pettis integrals
The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...
On derivations on certain function spaces and their relation to the differential operator. (Über Derivationen auf gewissen Funktionenräumen und deren Beziehung zum Differentiationsoperator.)