Erhan Deniz - Academia.edu (original) (raw)

Papers by Erhan Deniz

Hacettepe University Bulletin of Natural Sciences and Engineering Series B Mathematics and Statistics, 2012

The main object of the present paper is to derive several sufficient conditions for close-to-conv... more The main object of the present paper is to derive several sufficient conditions for close-to-convexity, starlikeness, and convexity of certain p-valent analytic functions in the unit disk. Some interesting consequences of the main results are also mentioned.

arXiv (Cornell University), Mar 9, 2011

In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the anal... more In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the analyticity and the univalence of the functions defined by an integral operator. These conditions involves Ruscheweyh and Sȃlȃgean derivative operator in the open unit disk. In particular cases, we find the well-known conditions for univalency established by Becker [3], Ahlfors [2], Kanas and Srivastava [8] and others for analytic mappings f : U → C. Also, we obtain the corresponding new, useful and simpler conditions for this integral operator.

In this paper, sharp upper bounds for ap+2 a 2+1 and |ap+3| are derived for a class of Mocanu -co... more In this paper, sharp upper bounds for ap+2 a 2+1 and |ap+3| are derived for a class of Mocanu -convex p-valent functions defined by an extended linear multiplier dierential operator (LMDO)

Journal of Classical Analysis, 2014

Making use of the method of subordination chains, we obtain some sufficient conditions for the un... more Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a quasiconformal extension criterion of the main result, is also obtained.

Mathematical Inequalities & Applications, 2016

In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel func... more In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some Mittag-Leffler expansions for the derivatives of Bessel functions of the first kind, as well as some results on the zeros of these functions.

Kyungpook mathematical journal, 2010

In this present work, the authors obtain Fekete-Szegö inequality for certain normalized analytic ... more In this present work, the authors obtain Fekete-Szegö inequality for certain normalized analytic function f (z) defined on the open unit disk for which (1−α)z(D m λ,µ f (z)) +αz(D m+1 λ,µ f (z)) (1−α)D m λ,µ f (z)+αD m+1 λ,µ f (z) (λ ≥ µ ≥ 0, m ∈ N0, α ≥ 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szegö inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to generalize the Fekete-Szegö inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator D m λ,µ .

Mathematische Nachrichten, 2016

In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some ... more In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some newly discovered Mittag-Leffler expansions for Bessel functions of the first kind.

Applied Mathematics and Computation, 2015

In the present investigation the authors obtain upper bounds for the second Hankel determinant H ... more In the present investigation the authors obtain upper bounds for the second Hankel determinant H 2 (2) of the classes bi-starlike and bi-convex functions of order β, represented by S * σ (β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinant H 2 (2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.

Mathematical Inequalities & Applications, 2015

The aim of the present paper determine the ratio of the normalized Lommel functions L μ,ν of the ... more The aim of the present paper determine the ratio of the normalized Lommel functions L μ,ν of the form (??) to its sequence of partial sums L μ,ν m (z) = z + m ∑ n=1 a n z n+1 when the coefficients of L μ,ν satisfy some conditions. Furthermore we investigate the radii of univalency, starlikeness, convexity and close-to-convexity of the partial sums L μ,ν m (z). Computational and graphical usages of Maple (Version 17) as well as geometrical descriptions of the image domains in several illustrative examples are also presented.

Journal of Advances in Applied & Computational Mathematics, 2015

The object of the present paper is to derive new coefficient inequalities for certain subclasses ... more The object of the present paper is to derive new coefficient inequalities for certain subclasses of p - valent analytic functions defined in the open unit disk U. Our results are generalized of the previous theorems given by J. Clunie and F.R. Keogh [1], by H. Silverman [3] and by M. Nunokawa et al. [2].

The main object of this paper is to give sufficient conditions for integral operators H α,β,γ and... more The main object of this paper is to give sufficient conditions for integral operators H α,β,γ and G λ,µ , which are defined here by means of the meromorphic functions, to be univalent in the open unit disk. In particular cases, we find the corresponding simpler conditions for these integral operators.

In this paper, we define two new general p-valent integral operators in the unit disc U, and obta... more In this paper, we define two new general p-valent integral operators in the unit disc U, and obtain the convexity properties of these integral operators of p-valent functions on some classes of β-uniformly p-valent starlike and β-uniformly p-valent convex functions of complex order. As special cases, the convexity properties of the operators z 0 f (t) t µ dt and z 0 (g ′ (t)) µ dt are given.

Kodai Mathematical Journal, 2012

ABSTRACT By using Dziok-Srivastava operator a new subclass of analytic functions generalized k-pa... more ABSTRACT By using Dziok-Srivastava operator a new subclass of analytic functions generalized k-parabolic starlike functions, denoted by k–SPl,m (α1;γ), is introduced. For this class the Fekete-Szegö problem is completely solved. Various known or new special cases of our results are also point out.

Filomat, 2013

In the present investigation, we study the majorization properties for certain classes of multiva... more In the present investigation, we study the majorization properties for certain classes of multivalent analytic functions defined by using the generalized Noor integral operator. Moreover, we point out some new or known consequences of our main result.

Czechoslovak Mathematical Journal, 2010

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Computers & Mathematics with Applications, 2011

In this paper we introduce and study two new subclasses Σ λµmp (α, β) and Σ + λµmp (α, β) of mero... more In this paper we introduce and study two new subclasses Σ λµmp (α, β) and Σ + λµmp (α, β) of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of (n, δ)−neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.

Arabian Journal for Science and Engineering, 2011

In the present paper the new multiplier transformations J δ p (λ, µ, l) (δ, l ≥ 0, λ ≥ µ ≥ 0; p ∈... more In the present paper the new multiplier transformations J δ p (λ, µ, l) (δ, l ≥ 0, λ ≥ µ ≥ 0; p ∈ N) of multivalent functions is defined. Making use of the operator J δ p (λ, µ, l), two new subclasses P δ λ,µ,l (A, B; σ, p) and P δ λ,µ,l (A, B; σ, p) of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses P δ λ,µ,l (A, B; σ, p) and P δ λ,µ,l (A, B; σ, p) are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.

Applied Mathematics Letters, 2012

In this paper, we introduce a new general integral operator defined by the Hadamard product. Furt... more In this paper, we introduce a new general integral operator defined by the Hadamard product. Furthermore, we obtained new sufficient conditions for this operator to be univalent in the open unit disk.

Annales UMCS, Mathematica, 2010

The main object of the present paper is to extend the univalence condition for a family of integr... more The main object of the present paper is to extend the univalence condition for a family of integral operators. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided. Recently, Frasin and Darus (see [6]) defined and studied the class B(γ). In his paper Frasin (see [4]) obtained some results for functions belonging 2000 Mathematics Subject Classification. 30C45.