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In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions which both f ⁢ (z) and f - 1 ⁢ (z) are m-fold symmetric on the open unit disk. Furthermore, we find upper bounds for the initial coefficients | a m + 1 | and | a 2 ⁢ m + 1 | for functions in this subclass. The results presented in this paper generalize and improve some recent works [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on Δ = {z ∈ ℂ: 1 < |z| < ∞}. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper generalize and improve some recent works.

In the first part of this work we present several new geometric properties of analytic functions by applying the differential subordination. In addition, several results in the geometric functions theory pointed out. In the second part we find upper bounds for coefficients of functions in class B∑q,µ (β, λ, h) which is defined by fractional q-calculus operators. [ABSTRACT FROM AUTHOR]

Hankel matrices are related to a wide range of disparate determinant computations and algorithms and some very attractive computational properties are allocated to them. Also, the Hankel determinants are crucial factors in the research of singularities and power series with integral coefficients. It is specified that the Fekete-Szegö functional and the second Hankel determinant are equivalent to H1(2) and H2(2), respectively. In this study, the upper bounds were obtained for the second Hankel determinant of the subclass of bi-univalent functions, which is defined by subordination. It is worth noticing that the bounds rendered in the present paper generalize and modify some previous results. [ABSTRACT FROM AUTHOR]

In this work, the Faber polynomial expansions and a different method were employed to estimate the |an| coefficients of a subclass of bi-close-to-convex functions, which is introduced by subordination concept in the open unit disk. Further, we generalize some of the previous outcomes. [ABSTRACT FROM AUTHOR]

In this work, we firstly introduce a new subclass B∑h(n,λ) of analytic and biunivalent functions. Moreover, we estimate the second and third coefficients for functions in this subclass. Our results presented in this paper improve some recent works. [ABSTRACT FROM AUTHOR]

In this paper, we use the Faber polynomial expansion to find upper bounds for |an | (n ≥ 3) coefficients of functions belong to classes HqΣ(λ, h), STqΣ(α, h) and MqΣ (α, h) which are defined by quasi-subordinations in the open unit disk U. Further, we generalize some of the previously published results. [ABSTRACT FROM AUTHOR]

Let p(z) be a polynomial of degree n, and Dαp(z) be its polar derivative of p(z). Dewan et al proved that if p(z) has all its zeros in | z |≤ k, (k ≤ 1), with s -fold zeros at the origin then for every α ∈ ℂ with | α |≥ k and for each r >0,In this paper, we obtain a refinement for above inequality. Also we extend some in-equalities for a polynomial of the form . [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of some common best proximity point theorems for generalized Lipschitz contractive mappings on cone b-metric spaces over Banach algebras without assumption of normality. Our results generalize the corresponding result by Xu and Radenović (Fixed Point Theory and Appl. 2014, 2014: 102) and by Huang and Radenović (J. Computational Anal. and Appl. 2016, 20(3)). Further, we give an example to illustrate that our works are never equivalent with the counterparts in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we find coefficient estimates by a new method making use of the Faber polynomial expansions for a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. The coefficient bounds presented in this paper would generalize and improve some recent works appeared in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate an interesting subclass of analytic and bi-univalent functions in the open unit disk U. Furthermore, we find upper bounds for the second and third coefficients for functions in this subclass. The results presented in this paper would generalize and improve some recent works. [ABSTRACT FROM AUTHOR]

In this paper, we have presented some common fixed point results for the contractive mappings on complex valued bmetric spaces and obtained a generalization of the theorem of Azam et al., [2], Klin-eam and Suanoom [7], Mukheimer [8], Rouzkard and Imdad [12], Sitthikul and Saejung [13] and Sintunavarat and Kumam[14]. Further, our result is supported by examples. [ABSTRACT FROM AUTHOR]

For a polynomial p(z) of degree n, we consider an operator Da which map a polynomial p(z) into Dap(z) := (a - z)p′(z) + np(z) with respect to a. It was proved by Liman et al. (2010) that if p(z) has no zeros in |z| < 1, then for all a, ß ε C with |a| = 1, |ß| = 1 and |z| = 1, |zDap(z)+nß((|a|-1)/2)p(z)| = (n/2){［|a+ß((|a|-1)/2)|+|z+ß((|a|-1)/2)|］max|z|=1|p(z)|-［|a+ ß((|a| - 1)/2)| - |z + ß((|a| - 1)/2)|］min|z|=1|p(z)|}. In this paper we extend the above inequality for the polynomials having no zeros in |z| < k, where k = 1. Our result generalizes certain well-known polynomial inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some results on common best proximity points for non-self mappings between two subsets of complex valued b-metric spaces. For this purpose, first we generalize some well-known results that were proved in classic metric spaces on complex valued b-metric space by some new definitions. Second we present a type of contractive condition and develop a common best proximity point theorem for non-self mappings in complex-valued b-metric spaces. Our results are supported by some examples. [ABSTRACT FROM AUTHOR]