Anastassiou, G. A.
Most general fractional representation formula for functions and
implications
(pp. 89−98)
A B S T R A C T S
TILING 3 AND 4DIMENSIONAL EUCLIDEAN SPACES BY LEE SPHERES
Sándor Szabó
sszabo7@hotmail.com
2000 Mathematics Subject Classification:
Primary 94B60; Secondary 05B45, 52C22.
Key words:
tiling by Lee spheres, integer tiling, latticelike tiling, exact cover problem.
The paper addresses the problem if the ndimensional Euclidean space can
be tiled with translated copies of Lee spheres of not necessarily equal radii such that at least one of the Lee spheres has radius at least 2.
It will be showed that for n = 3, 4 there is no such tiling.
SUFFICIENT CONDITION FOR STRONGLY STARLIKE AND CONVEX FUNCTIONS
Rahim Kargar
rkargar1983@gmail.com,
kargarmath@ymail.com,
Rasoul Aghalary
raghalary@yahoo.com,
r.aghalary@urmia.ac.ir
2000 Mathematics Subject Classification:
Primary 30C45; Secondary 30C80.
Key words:
Analytic functions, strongly starlike, strongly convex, univalent, multivalent.
In this paper, we obtain sufficient conditions for
analytic functions f(z) in the open unit disk Δ to be
strongly starlike and strongly convex of order β and type
α. Some interesting corollaries of the results presented here
are also discussed.
PELL FORM AND PELL EQUATION VIA OBLONG
NUMBERS
Kuldip Raj
kuldeepraj68@rediffmail.com,
Sunil K. Sharma
sunilksharma42@yahoo.co.in
2000 Mathematics Subject Classification:
40A05, 46A45, 46E30.
Key words:
Orlicz function, MusielakOrlicz function, Lacunary sequence, $n$normed spaces, paranorm space.
In the present paper we introduce some multiplier sequence spaces over nnormed spaces defined by a MusielakOrlicz function M = (M_{k}). We also study some topological properties and some inclusion relations between these spaces.
ON THE SETTHEORETIC COMPLETE INTERSECTION PROPERTY FOR THE EDGE IDEALS OF WHISKER GRAPHS
Antonio Macchia
macchia@dm.uniba.it
2000 Mathematics Subject Classification:
13A15, 13F55, 14M10, 05C05, 05C38.
Key words:
Settheoretic complete intersection ideals, arithmetical rank, edge ideals, whiskers, sunlet graphs, cactus graphs.
We show that the edge ideals of some whisker graphs are settheoretic complete intersections.
INTERVAL CRITERIA FOR FORCED OSCILLATION OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH γLAPLACIAN, DAMPING AND MIXED NONLINEARITIES
E. ElShobaky
e_elshobaky@hotmail.com,
E. M. Elabbasy
emelabbasy@mans.edu.eg,
T. S. Hassan
tshassan@mans.edu.eg,
B. A. Glalah
b.glalah@yahoo.com
2000 Mathematics Subject Classification:
34C10, 34C15.
Key words:
Interval criteria, forced Oscillation, $\gamma $Laplacian,
nonlinear functional differential equations.
We consider a forced second order functional differential equation with γLaplacian, damping, and mixed nonlinearities in the form of
(r(t)Φ_{γ}(x′(t)))′
+p(t)Φ_{γ}(x′(t))
+q_{0}(t)Φ_{β}(x(t))+
∫^{a}_{b}
q(t,s)Φ_{α(s)}(x(g(t,s)))dζ(s) = e(t), 

where γ, β ∈ [0, ∞),
− ∞ < a < b ≤ ∞,
α ∈ C[a, b) is strictly increasing is such that
0 ≤ α (a) < μ < α (b−) with
β > γ > μ > 0; r, p, q_{0},
e ∈ C([t_{0}, ∞), R) with r(t) > 0 on [t_{0}, ∞); q ∈ C([0, ∞) × [a, b));
and ζ : [a, b) → R is nondecreasing. The function g ∈ C([0, ∞) × [a, b), [0, ∞)) is such that
lim_{t → ∞} g(t,s) = ∞, for s ∈ [a, b). Interval oscillation criteria of the ElSayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments.
EMPIRICAL BAYES TEST FOR THE PARAMETER OF EXPONENTIALWEIBULL DISTRIBUTION UNDER NEGATIVE ASSOCIATED SAMPLES
Naiyi Li
linaiyi1979@163.com,
Yongming Li
lym1019@163.com
2000 Mathematics Subject Classification:
62C12, 62F12.
Key words:
Negative associated samples; empirical Bayes test; asymptotic optimality; convergence rates.
By using weighted kerneltype density estimator, the empirical Bayes test rules for parameter of ExponentialWeibull distribution are constructed and the asymptotically optimal property is obtained under negative associated samples. It is shown that the convergence rates of the proposed EB test rules can arbitrarily close to O(n^{−1/2}) under very mild conditions.
MOST GENERAL FRACTIONAL REPRESENTATION FORMULA FOR FUNCTIONS AND
IMPLICATIONS
George A. Anastassiou
ganastss@memphis.edu
2000 Mathematics Subject Classification:
26A33, 26D10, 26D15.
Key words:
Fractional representation, Kalla fractional integral, Ostrowski inequality.
Here we present the most general fractional representation formulae for a
function in terms of the most general fractional integral operators due to
S. Kalla, [On operators of fractional integration, I.
Math. Notae 22 (1970/71), 89−93],
[On operators of fractional integration, II.
Math. Notae 25, 1976, 29−35],
[Operators of fractional integration. In:
Analytic Functions Kozubnik'1979, Proc. of Conference, Kozubnik, Poland, 19−25 April 1979 (Ed. J. Lawrynowicz), Lecture Notes of Math. vol. 798, Berlin, Heidelberg, New York, Springer, 1980, 258−280].
The last include most of the
wellknown fractional integrals such as of RiemannLiouville, ErdélyiKober and Saigo, etc. Based on these we derive very general fractional
Ostrowski type inequalities.
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