Some inequalities on Bazilevič class of functions involving quasi-subordination

Karthikeyan, K. R.; Murugusundaramoorthy, G.; Cho, N. E.

doi:10.3934/math.2021417

Cited by 8 publications

(3 citation statements)

References 23 publications

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“…Also, we have pointed out appropriate connections and applications of our main results, which are mostly presented in the form of corollaries and remarks. Refer to [5,23,25,[38][39][40], for studies closely related to the results presented here.…”

Section: Discussionmentioning

confidence: 99%

Unified Solution of Some Properties Related to λ-Pseudo Starlike Functions

Ibrahim,

Karthikeyan

2023

Contemp. Math.

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To unify and extend the study of various subclasses of starlike and convex functions, here we introduce a new subclass of λ-pseudo starlike symmetric functions. To add more versatility to our study, we have defined a new class of functions subordinate to a conic region impacted by the well-known Janowski functions. This study extends well-known results and unifies the studies of various subclasses of α-convex functions. Coefficient estimates of the inverse function and the Fekete-Szegő result for the function class are the main results. Some interesting special cases of our main results are also presented here.

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Section: Discussionmentioning

confidence: 99%

Unified Solution of Some Properties Related to λ-Pseudo Starlike Functions

Ibrahim,

Karthikeyan

2023

Contemp. Math.

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“…Motivated by [11][12][13][14][15][16][17], we now define a generalized class of Bazilevič functions.…”

Section: Convex and Starlike In One Directionmentioning

confidence: 99%

On Classes of Non-Carathéodory Functions Associated with a Family of Functions Starlike in the Direction of the Real Axis

Karthikeyan

Cho

Murugusundaramoorthy

2022

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“…They have introduced the starlikeness and convexity sub-classes. These classes were modified later considering other collection of analytic functions, generalized by assuming any types of differential or integral operators and extended including fractional operators in the open unit disk (see [11][12][13][14][15][16]). In our investigation, we formulate the suggested class using the Ma-Minda-Janowski inequality.…”

Section: Introductionmentioning

confidence: 99%

On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

Alarifi

Ibrahim

2021

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(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

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Some inequalities on Bazilevič class of functions involving quasi-subordination

Cited by 8 publications

References 23 publications

Unified Solution of Some Properties Related to λ-Pseudo Starlike Functions

Unified Solution of Some Properties Related to λ-Pseudo Starlike Functions

On Classes of Non-Carathéodory Functions Associated with a Family of Functions Starlike in the Direction of the Real Axis

On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

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