2021-01-28T06:29:26Z
http://www.kjm-math.org/?_action=export&rf=summon&issue=5580
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Stability Results for Neutral Integro-Differential Equations with Multiple Functional Delays
Ernest
Yankson
Necessary and sufficient conditions for the zero solution of the nonlinear neutral integro-differential equation\begin{eqnarray*}&&\frac{d}{dt}\Big(r(t)\Big[x(t)+Q(t, x(t-g_1(t)),...,x(t-g_N(t)))\Big]\Big)\\ &&= -a(t)x(t)+ \sum^{N}_{i=1}\int^{t}_{t-g_i(t)}k_i(t,s)f_i(x(s))ds \end{eqnarray*} to be asymptotically stable are obtained. In the process we invert the integro-differential equation and obtain an equivalent integral equation. The contraction mapping principle is used as the main mathematical tool for establishing the necessary and sufficient conditions.
Stability
integro-differential equation
functional delay
2017
01
01
1
11
http://www.kjm-math.org/article_43831_2161050be631ca19a702fe6a0bd6d1c3.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Periodic Solutions for Third-Order Nonlinear Delay Differential Equations with Variable Coefficients
Abdelouaheb
Ardjouni
Farid
Nouioua
Ahcene
Djoudi
In this paper, the following third-order nonlinear delay differential equationwith periodic coefficients%\begin{align*}& x^{\prime\prime\prime}(t)+p(t)x^{\prime\prime}(t)+q(t)x^{\prime}(t)+r(t)x(t)\\& =f\left( t,x\left( t\right) ,x(t-\tau(t))\right) +\frac{d}{dt}g\left(t,x\left( t-\tau\left( t\right) \right) \right) ,\end{align*}is considered. By employing Green's function, Krasnoselskii's fixed pointtheorem and the contraction mapping principle, we state and prove theexistence and uniqueness of periodic solutions to the third-order nonlineardelay differential equation.
fixed point
periodic solutions
third-order nonlinear delay differential equations
2017
01
01
12
21
http://www.kjm-math.org/article_44493_fca28ec0388a064bcfebffd47c16b12f.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Operators Reversing Orthogonality and Characterization of Inner Product Spaces
Paweł
Wójcik
In this short paper we answer a question posed by Chmieliński in [Adv. Oper. Theory, 1 (2016), no. 1, 8-14]. Namely, we prove that among normed spaces of dimension greater than two,only inner product spaces admit nonzero linear operators which reverse the Birkhoff orthogonality.
Birkhoff orthogonality
orthogonality reversing mappings
characterizations of inner product spaces
2017
01
01
22
24
http://www.kjm-math.org/article_44746_9f829bbb7fc2df9483fd2622f9084732.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Certain Properties of a Subclass of Univalent Functions With Finitely Many Fixed Coefficients
S.Sunil
Varma
Thomas
Rosy
In this paper a new class of analytic, univalent and normalized functions with finitely many fixed coefficients is defined. Properties like coefficient condition, radii of starlikeness and convexity, extreme points and integral operators applied to functions in the class are investigated.
Analytic function
univalent function
fixed coefficient
Extreme point
2017
01
01
25
32
http://www.kjm-math.org/article_44920_245bef22255f8b0b38f19d4c0c83a25b.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
On Para-Sasakian Manifolds Satisfying Certain Curvature Conditions with Canonical Paracontact Connection
Selcen
Yüksel Perktaş
In this article, the aim is to introduce a para-Sasakian manifold with acanonical paracontact connection. It is shown that $\varphi$-conharmonically flat, $\varphi $-$W_{2}$ flat and $\varphi $-pseudo projectively flat para-Sasakian manifolds with respect to canonical paracontact connection are all $\eta $-Einsteinmanifolds. Also, we prove that quasi-pseudo projectively flatpara-Sasakian manifolds are of constant scalar curvatures.
Canonical connection
paracontact metric structure
normal structure
2017
01
01
33
43
http://www.kjm-math.org/article_45190_7d44a17d67db3000195bfd95cc73a650.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Approximation for a Summation-Integral Type Link Operators
Arun
Kajla
The present article deals with the general family of summation-integral type operators. Here, we propose the Durrmeyer variant of the generalized Lupaş operators considered by Abel and Ivan (General Math. 15 (1) (2007) 21-34) and study local approximation, Voronovskaja type formula, global approximation, Lipchitz type space and weighted approximation results. Also, we discuss the rate of convergence for absolutely continuous functions having a derivative equivalent with a function of bounded variation.
Global approximation
Rate of convergence
Modulus of continuity
bounded variation
2017
01
01
44
60
http://www.kjm-math.org/article_45322_725917aec0e6b1c459fe81fc2e4d7411.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Ostrowski's Inequality for Functions whose First Derivatives are $s$-Preinvex in the Second Sense
Badreddine
Meftah
In this paper, we establish some new Ostrowski type inequalities forfunctions whose first derivatives are $s$-preinvex in the second sense.
Ostrowski inequality
midpoint inequality
H"{o}lder inequality
power mean inequality
preinvex functions
$s$-preinvex functions
2017
01
01
61
80
http://www.kjm-math.org/article_46863_69c7dd0b531fa53298dd16c90cd3a0f8.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2017
3
1
Proximal Point Algorithms for Numerical Reckoning Fixed Points of Hybrid-Type Multivalued Mappings in Hilbert Spaces
Kritsada
Lerkchaiyaphum
Withun
Phuengrattana
In this paper, we propose a new iteration process to approximateminimizers of proper convex and lower semi-continuous functions andfixed points of $\lambda$-hybrid multivalued mappings in Hilbertspaces. We also provide an example to illustrate the convergencebehavior of the proposed iteration process and numerically comparethe convergence of the proposed iteration scheme with the existingschemes.
Proximal point algorithm
hybrid multivalued mapping
Ishikawa iteration
S-iteration
Hilbert spaces
2017
01
01
81
89
http://www.kjm-math.org/article_46951_9c228d2ed70ca44facd3ac48e7b8797e.pdf