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Adem Kilicman

Publications and source records attributed to Adem Kilicman.

29 records · Page 2Linked to original sources
arXiv2015

A de Casteljau Algorithm for Bernstein type Polynomials based on (p,q)-integers

In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier curves based on (p,q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) \in [0, 1] \times [0, 1] depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. Furthermore, some fundamental properties for (p,q)-Bernstein Bezier curves are discussed. We get q-Bezier curves and surfaces for (u, v) \in [0, 1] \times [0, 1] when we set the parameter p1 = p2 = 1.

cs.GR↗
arXiv2015

Bezier curves and surfaces based on modified Bernstein polynomials

In this paper, we use the blending functions of Bernstein polynomials with shifted knots for construction of Bezier curves and surfaces. We study the nature of degree elevation and degree reduction for Bezier Bernstein functions with shifted knots. Parametric curves are represented using these modified Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We get Bezier curve defined on [0, 1] when we set the parameter α=βto the value 0. We also present a de Casteljau algorithm to compute Bernstein Bezier curves and surfaces with shifted knots. The new curves have some properties similar to Bezier curves. Furthermore, some fundamental properties for Bernstein Bezier curves and surfaces are discussed.

cs.GR↗
arXiv2015

A Novel Subclass of Analytic Functions Specified by a Family of Fractional Derivatives in the Complex Domain

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{τ,μ}(k,δ,γ)$ of analytic and univalent functions in the open unit disk $\mathbb{U}$. In particular, for functions in the class $\mathcal{P}_{τ,μ}(k,δ,γ)$, we derive sufficient coefficient inequalities, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class $\mathcal{P}_{τ,μ}(k,δ,γ)$ are also pointed out.

math.CV↗
arXiv2015

Mixed solutions of monotone iterative technique for hybrid fractional differential equations

This paper concerns with a mathematical modelling of biological experiments, and its influence on our lives. Fractional hybrid iterative differential equations are equations that interested in mathematical model of biology. Our technique is based on the Dhage fixed point theorem. This tool describes mixed solutions by monotone iterative technique in the nonlinear analysis. This method is used to combine two solutions: lower and upper. It is shown an approximate result for the hybrid fractional differential equations iterative in the closed assembly formed by the lower and upper solutions.

math.CA↗
arXiv2015

Statistical approximation properties of Stancu type $q$-Baskakov-Kantorovich operators

In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type function are also established for said operators. Finally, we construct a bivariate generalization of the operator and also obtain the statistical approximation properties.

math.CA↗
arXiv2015

On Pairwise paralindeloff Bitopological Spaces

The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are investigated and studied. Furthermore, the relation of among them with some pairwise separation axioms are considered.

math.GN↗
arXiv2013

Parameterized Norm and Parameterized Fixed-Point Theorem by Using Fuzzy Soft Set Theory

From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set theory, called fuzzy soft set theory, by Maji et.al opened a new way for researchers whose frame work of study is soft sets and fuzzy sets. Although published papers in this area have considered both application and theoretical aspects of fuzzy soft set theory, the concept of norm for a fuzzy soft set has not been studied yet. We begin this paper by introducing fuzzy soft real numbers, which are needed for study fuzzy soft norm, and then continued by considering fuzzy soft norm. Fixed-point theorem is also investigated for fuzzy soft normed spaces.

math.FA↗
arXiv2010

Some applications for Fadell-Dold theorm in fibration theory by using homotopy groups

The purpose of this paper is to give some solutions for the classification problem in fibration theory by using the homotopy sequences of fibrations (sequences of $n$-th homotopy groups $ π_{n}(S,s_{o}) $ of total spaces of fibrations). In particular, to show the role of homotopy sequence of $n$-th homotopy to get the required fiber map in Fadell-Dold theorem such that the restriction of this fiber map on some fiber spaces is a homotopy equivalence.

math.AT↗
arXiv2010

On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

Let $f:E\longrightarrow O$ be a Hurewicz fibration with a fiber space $F_{r_{o}}$ and a lifting function $L_{f}$. The \emph{$Lf-$function} $Θ_{L_{f}}$ of $f$ is defined by the restriction map of $L_{f}$ on the space $Ω(O,r_{o})\times F_{r_{o}}\times \{1\}$. The purpose of this paper is to give some results which show the role of $Lf-$functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of polyhedron spaces.

math.AT↗
arXiv2009

On The Pairwise Weakly Lindelof Bitopological Spaces

In this paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, investigate some of their properties and show that a pairwise weakly Lindelof property is not a hereditary property.

math.GN↗