Khayyam Journal of MathematicsKhayyam Journal of Mathematics
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Mon, 22 Jan 2018 23:25:56 +0100FeedCreatorKhayyam Journal of Mathematics
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Feed provided by Khayyam Journal of Mathematics. Click to visit.Approximation with Certain SzĂˇszâ€“Mirakyan Operators
http://www.kjm-math.org/article_47347_5579.html
In the current article, we consider different growth conditions for studying the well known Szász–Mirakyan operators, which were introduced in the mid-twentieth century. Here, we obtain a new approach to find the moments using the concept of moment generating functions. Further, we discuss a uniform estimate and compare convergence behavior with the recently studied one.Sat, 30 Sep 2017 20:30:00 +0100Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space ...
http://www.kjm-math.org/article_51873_0.html
We present a local convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative. Numerical examples are also provided in this study.Mon, 06 Nov 2017 20:30:00 +0100New Inequalities of Hermite-Hadamard Type for Log-Convex Functions
http://www.kjm-math.org/article_47458_5579.html
Some new inequalities of Hermite-Hadamard type for log-convex functions defined on real intervals are given.Sat, 30 Sep 2017 20:30:00 +0100The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
http://www.kjm-math.org/article_53432_0.html
This paper describes the classification of the $n$-fold symmetric product of a finite graph by means of its homotopy type, having as universal models the $n$-fold symmetric product of the wedge of $n$-circles; and introduces a CW-complex called $binomial torus$, which is homeomorphic to a space that is a strong deformation retract of the second symmetric products of the wedge of $n$-circles. Applying the above we calculate the fundamental group, Euler characteristic, homology and cohomology groups of the second symmetric product of finite graphs.Mon, 27 Nov 2017 20:30:00 +0100Linear Preservers of Right SGUT-Majorization on $\mathbb{R}_{n}$
http://www.kjm-math.org/article_49229_5579.html
A matrix $R$ is called a $textit{generalized row substochastic}$ (g-row substochastic) if the sum of entries on every row of $R$ is less than or equal to one. For $x$, $y in mathbb{R}_{n}$, it is said that $x$ is $textit{rsgut-majorized}$ by $y$ (denoted by $ x prec_{rsgut} y$ ) if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $x=yR$. In the present paper, we characterize the linear preservers and strong linear preservers of rsgut-majorization on$mathbb{R}_{n}$.Sat, 30 Sep 2017 20:30:00 +0100A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
http://www.kjm-math.org/article_53655_0.html
The aim of this paper is to introduce a new class of harmonic functionsdefined by use of a subordination. We find necessary and sufficientconditions, radii of starlikeness and convexity and compactness for thisclass of functions. Moreover, by using extreme points theory we also obtaincoefficients estimates, distortion theorems for this class of functions. Onthe other hand, some results (corollaries) on the paper are pointed out.Sat, 02 Dec 2017 20:30:00 +0100A Class of Sequence Spaces Defined by Fractional Difference Operator and Modulus Function
http://www.kjm-math.org/article_49370_5579.html
A class of vector-valued sequence spaces is introduced employing the fractional difference operator $Delta^{(alpha)}$, a sequence of modulus functions and a non-negative infinite matrix. Sequence spaces of this class generalize many sequence spaces which are defined by difference operators and modulus functions. It is proved that the spaces of this class are complete paranormed spaces under certain conditions. Some properties of these spaces are studied and it is shown that the spaces are not solid in general.Sat, 30 Sep 2017 20:30:00 +0100Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$-Preinvex Functions
http://www.kjm-math.org/article_54680_0.html
In the present paper, the notion of generalized beta $(r,g)$-preinvex function is applied for establish some new generalizations of Ostrowski type inequalities via fractional integral operators. These results not only extend the results appeared in the literature [43] but also provide new estimates on these type. At the end, some applications to special means are given.Sat, 30 Dec 2017 20:30:00 +0100Approximation by Stancu Type Generalized Srivastava-Gupta Operators Based On Certain Parameter
http://www.kjm-math.org/article_49477_5579.html
In the present paper, we introduce a Stancu type generalization of generalized Srivastava-Gupta operators based on certain parameter. We obtain the moments of the operators and then prove the basic convergence theorem. Next, the Voronovskaja type asymptotic formula and some direct results for the above operators are discussed. Also, weighted approximation and rate of convergence by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimates using the Lipschitz type maximal function. Lastly, we propose a King type modification of these operators to obtain better estimates.Sat, 30 Sep 2017 20:30:00 +0100Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
http://www.kjm-math.org/article_55158_0.html
This paper contains two improvements on a theorem of S. N. Bernstein for Banach spaces. We show that if $X$ is an arbitrary infinite-dimensional Banach space, ${Y_n}$ is a sequence of strictly nested subspaces of $ X$ and if ${d_n}$ is a non-increasing sequence of non-negative numbers tending to 0, then for any $cin(0,1]$ we can find $x_{c} in X$, such that the distance $rho(x_{c}, Y_n)$ from $x_{c}$ to $Y_n$ satisfies$$c d_n leq rho(x_{c},Y_n) leq 4c d_n,~mbox{for all $ninmathbb N$}.$$We prove the above inequality by first improving Borodin (2006)'s result for Banach spaces by weakening his condition on the sequence ${d_n}$. The weakened condition on $d_n$ requires refinement of Borodin's construction to extract an element in $X$, whose distances from the nested subspaces are precisely the given values $d_n$.Sun, 07 Jan 2018 20:30:00 +0100Strong Differential Subordinations for Higher-Order Derivatives of Multivalent Analytic ...
http://www.kjm-math.org/article_50396_5579.html
In the present paper, we introduce and study a new class of higher-order derivatives multivalent analytic functions in the open unit disk and closed unit disk of the complex plane by using linear operator. Also we obtain some interesting properties of this class and discuss several strong differential subordinations for higher-order derivatives of multivalent analytic functions.Sat, 30 Sep 2017 20:30:00 +0100Holomorphic Structure of Middle Bol Loops
http://www.kjm-math.org/article_51111_5579.html
A loop $(Q,cdot,backslash,/)$ is called a middle Bol loop if it obeys the identity $x(yzbackslash x)=(x/z)(ybackslash x)$.To every right (left) Bol loop corresponds a middle Bol loop via an isostrophism. In this paper, the structure of the holomorph of a middle Bol loop is explored. For some special types of automorphisms, the holomorph of a commutative loop is shown to be a commutative middle Bol loop if and only if the loop is a middle Bol loop and its automorphism group is abelian and a subgroup of both the group of middle regular mappings and the right multiplication group. It was found that commutativity (flexibility) is a necessary and sufficient condition for holomorphic invariance under the existing isostrophy between middle Bol loops and the corresponding right (left) Bol loops. The right combined holomorph of a middle Bol loop and its corresponding right (left) Bol loop was shown to be equal to the holomorph of the middle Bol loop if and only if the automorphism group is abelian and a subgroup of the multiplication group of the middle Bol loop. The obedience of an identity dependent on automorphisms was found to be a necessary and sufficient condition for the left combined holomorph of a middle Bol loop and its corresponding left Bol loop to be equal to the holomorph of the middle Bol loop.Sat, 30 Sep 2017 20:30:00 +0100New Properties Under Generalized Contractive Conditions
http://www.kjm-math.org/article_51180_5579.html
The aim of this contribution is to establish some common fixed pointtheorems for single and set-valued maps under contractive conditions ofintegral type on a symmetric space. These maps are assumed to satisfy newproperties which extend the results of Aliouche [3], Aamri and ElMoutawakil [2] and references therein, also they generalize thenotion of non-compatible and non-$delta$-compatible maps in the setting ofsymmetric spaces.Sat, 30 Sep 2017 20:30:00 +0100