2017
DOI: 10.22190/fumi1702255a
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Subordination Conditions for a Class of Non-Bazilevič Type Defined by Using Fractional Q-Calculus Operators

Abstract: Abstract. In this article, we introduce and investigate a new class of non-Bazilevič functions with respect to k-symmetric points defined by using fractional q-calculus operators and q-differentiation. Several interesting subordination results are derived for the functions belonging to this class in the open unit disc. Furthermore, we point out some new and known consequences of our main result.

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Cited by 15 publications
(10 citation statements)
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“…Fractional calculus is an important branch of modern mathematical analysis and applications fields. [1][2][3][4][5][6][7][8] It plays an essential role in depicting complex nonlinear phenomena, [9][10][11][12][13][14] such as mathematical physics, fluid mechanics, viscoelastic mechanics, condensed matter physics, and neural network. In recent years, many fractional differential operators by considering the non-singular function as the kernel were constructed.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional calculus is an important branch of modern mathematical analysis and applications fields. [1][2][3][4][5][6][7][8] It plays an essential role in depicting complex nonlinear phenomena, [9][10][11][12][13][14] such as mathematical physics, fluid mechanics, viscoelastic mechanics, condensed matter physics, and neural network. In recent years, many fractional differential operators by considering the non-singular function as the kernel were constructed.…”
Section: Introductionmentioning
confidence: 99%
“…Several others have also released new classes of analytical functions with the resources of q-calculus operators. For any more inquiries on the analytic functions classes, we refer to [1,2,[8][9][10][11][12][13] for functions described by applying q-calculus operators and subject related to this work.…”
Section: Introduction and Preliminarymentioning
confidence: 99%
“…Anastassiu and Gal [22,23] also played their part in the development of complex variables with q-generalization. Purohit et al [24] have used fractional q-calculus operators to apply subordination conditions on the class of non-Bazilevic functions. Sahoo and Agrawal [25] worked on starlike functions in q-calculus and extended the idea of q-starlikeness for particular subclasses of starlike functions.…”
Section: Introductionmentioning
confidence: 99%