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This paper introduces two new subclasses of analytical functions with negative coefficients and derives coefficient estimates for these novel subclasses. Further, inclusion relations and necessary and sufficient conditions for the Poisson distribution series to belong to these subclasses are established. [ABSTRACT FROM AUTHOR]

In this paper we investigate a subclass M(α) of the class of starlike functions in the unit disk jzj < 1. M(α), Π/2 ≥ α < Π, is the set of all analytic functions f in the unit disk jzj < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition... The class M(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639-1649, 2017]. In this paper some basic geometric properties of the class M() are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szego functional associated with the k-th root transform [f(zk)]1/k. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we use the use the linear operator Ⳅ,σ x(u, v, y)f(z) and the concept of the subordination to analyse the general class of all analytic univalent functions. Our main results are implication properties between the classes of such functions and the application of these properties to special cases. [ABSTRACT FROM AUTHOR]

In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric q-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results. [ABSTRACT FROM AUTHOR]

In the present paper, we determine new characterisations of the sub-classes TS*C(α, β, γ) and TCC(; fi;) of analytic functions associated with Pascal distribution series ... mzn. Further, we give necessary and suficient conditions for an integral operator related to Pascal distribution series Gmq f(z) = R z 0 mq (t) t dt to belong to the above classes. Several corollaries and consequences of the main results are also considered. [ABSTRACT FROM AUTHOR]

The object of the present paper is to derive some inclusion and subordination results for certain classes of multivalent analytic functions in the open unit disk, which are defined in terms of the Cho-Kwon-Srivastava operator. Some interesting corollaries are derived and the relevant connection of the results obtained in this paper with various known results are also pointed out. [ABSTRACT FROM AUTHOR]

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate two new subclasses, namely; the class of strongly a-- bi-spirallike functions of order ß and a-- bi-spirallike functions of order p, of the function class £; of normalized analytic and bi-univalent functions in the open unit disk U = {z:z ă C and |z| < 1}. We find estimates on the coefficients |a2|, |a3| and |a4| for functions in these two subclasses. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by Salagean q-calculus operator in the open disk U. For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. Some consequences of the main results are also observed. [ABSTRACT FROM AUTHOR]

In the papers [5]-[7] was examined approximation of functions by the modified Szász-Mrakyan operators and other positive linear operators preserving e²(x) = x²: In this paper we introduce the Post-Widder and Stancu operators preserving x² in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce two novel subclasses Tμ(n, λ, α) and Hμ(n, λ, α; κ) of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, star-likenes, and convexity for the functions belonging to the class Tμ (n, λ, α). These results are then appropriately applied to derive similar geometrical properties for the other class Hμ(n, λ, α; κ) of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated. [ABSTRACT FROM AUTHOR]

In this paper, we have constructed subclasses of bi-univalent functions associated with λ-bi-pseudo-starlike functions in the unit disc U. Furthermore we established bound on the coe-cients for the subclasses Sλ Σ(k;α ) and Sλ Σ (k;βfi): [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce sufficient conditions for (Gaussian) hypergeometric functions to be in various subclasses of analytic functions. Also, we investigate several mapping properties involving these subclasses. [ABSTRACT FROM AUTHOR]

In this paper, we obtained some properties for subclasses of starlike functions defined by convolution such as partial sums, integral means, square root and integral transform for these classes. [ABSTRACT FROM AUTHOR]

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or T* is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on σ(T) and is not constant on each connected component of the open set U containing σ(T). (3) If E is the Riesz idempotent for a nonzero isolated point λ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and EH = N(T = λ) = N(T - λ)*. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Fekete-Szegö inequalities for certain subclasses of analytic univalent functions of complex order associated with quasi-subordination. [ABSTRACT FROM AUTHOR]

In the present paper, a new analytic function valued integral operator is introduced which is defined on n-copies of a subset of the class of normalized analytic functions on the unit disc of the complex plane. This operator, which is denoted here by Jαi, βi (f1, ..., fn)), unifies and generalizes several integral operators studied earlier. Inter- esting sufficient conditions are derived for the univalent starlikeness of Jαi, βi(f1, ..., fn)). [ABSTRACT FROM AUTHOR]

In the present paper, we introduce new subclasses of harmonic univalent functions and establish certain results concerning the convolution of functions for these subclasses. Relevant connections of the results presented here with various known results are briefly indicated. [ABSTRACT FROM AUTHOR]

In this paper we derive some results for certain new class of analytic functions defined by using Ruscheweyh derivative with varying arguments. [ABSTRACT FROM AUTHOR]

In this paper, we describe the characterizations of omega limit sets (= w-limit set) on ℝ² in detail. For a local real analytic flow Φ by z' = f(z) on ℝ², we prove the w-limit set from the basin of a given attractor is in the boundary of the attractor. Using the result of Jiménez-López and Llibre [9], we can completely understand how both the attractors and the w-limit sets from the basin. [ABSTRACT FROM AUTHOR]

The object of the present paper is to investigate the majorization properties of certain subclasses of analytic p-valent functions defined by convolution. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to obtain some subordination- and superordination- preserving properties for multivalent function associated the differintegral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich type theorem for the integral operator is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some applications of first order differential subordination and superordination results involving the operator Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed for certain normalized p-valent analytic functions associated with that operator. [ABSTRACT FROM AUTHOR]

In the present paper, we are concerned with subordination problems related to λ-Robertson function. The radii of λ-spirallikeness and starlikeness of λ-Robertson function are also determined. [ABSTRACT FROM AUTHOR]

In this paper, we define new classes of analytic functions using a general derivative operator which is a unification of the Sălăgean derivative operator, the Owa-Srivastava fractional calculus operator and the Al-Oboudi operator, and discuss some coefficient inequalities for functions belong to this classes. [ABSTRACT FROM AUTHOR]

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(Dλ,μm f(z))′ + αz (Dλ,μm+1 f(z))′/(1-α)(Dλ,μm f(z)+αDλ,μm+1 f(z) 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 Dλ,μm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results. [ABSTRACT FROM AUTHOR]

In this paper we consider some coefficient estimates in the subclass SL* of strongly starlike functions defined by a certain geometric condition. [ABSTRACT FROM AUTHOR]

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others. [ABSTRACT FROM AUTHOR]

In the present paper we introduce the subclass Saclambda (p,A,B) of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5]. [ABSTRACT FROM AUTHOR]