Some geometric properties of an integral operator involving Bessel functions

2017 ◽  
Vol 47 (2) ◽  
pp. 149-156
Author(s):  
Saurabh Porwal ◽  
Nanjundan Magesh ◽  
Surya Pratap Singh
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Geometric Properties

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

scholarly journals Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 719 ◽  
Author(s):  
Shahid Mahmood ◽  
Nusrat Raza ◽  
Eman S. A. AbuJarad ◽  
Gautam Srivastava ◽  
H. M. Srivastava ◽  
...  
Keyword(s):  
Integral Operator ◽  
Bessel Function ◽  
Analytic Functions ◽  
Operator Coefficient ◽  
Geometric Properties ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Inclusion Relations

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.

Geometric Properties of an Integral Operator

2016 ◽  
Vol 40 (1) ◽  
pp. 345-360
Author(s):  
Sarika Verma ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Integral Operator ◽  
Geometric Properties

scholarly journals Geometric Properties of a New Integral Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases.

scholarly journals A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shrideh Al-Omari ◽  
Dayalal Suthar ◽  
Serkan Araci
Keyword(s):  
Power Series ◽  
Integral Operator ◽  
Bessel Functions ◽  
Trigonometric Functions ◽  
Generating Series

AbstractThis paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various types of q-Bessel functions and some power series of special type. It has been obtained for basic q-generating series, q-exponential and q-trigonometric functions as well. Various results and corollaries are provided as an application to this theory.

scholarly journals Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications

2021 ◽  
Vol 7 (3) ◽  
pp. 3418-3439
Author(s):  
Jamshed Nasir ◽  
◽  
Shahid Qaisar ◽  
Saad Ihsan Butt ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Operator ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means ◽  
Special Cases ◽  
Derivatives Of ◽  
Quasi Convexity

<abstract><p>Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.</p></abstract>

scholarly journals Certain Geometric Properties of Lommel and Hyper-Bessel Functions

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 240
Author(s):  
Saima Mushtaq ◽  
Mohsan Raza ◽  
Muhey Din
Keyword(s):  
Bessel Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Geometric Properties ◽  
Lommel Functions

In this article, we are mainly interested in finding the sufficient conditions under which Lommel functions and hyper-Bessel functions are close-to-convex with respect to the certain starlike functions. Strongly starlikeness and convexity of Lommel functions and hyper-Bessel functions are also discussed. Some applications are also the part of our investigation.

scholarly journals On Geometric Properties of Normalized Hyper-Bessel Functions

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 316
Author(s):  
Khurshid Ahmad ◽  
Saima Mustafa ◽  
Muhey Din ◽  
Shafiq ur Rehman ◽  
Mohsan Raza ◽  
...  
Keyword(s):  
Hardy Spaces ◽  
Unit Disc ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Geometric Properties

In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc. We also study the Hardy spaces of hyper-Bessel functions.

scholarly journals ON NEW CLASSES OF ANALYTIC FUNCTIONS IMPOSED VIA THE FRACTIONAL ENTROPY INTEGRAL OPERATOR

2017 ◽  
pp. 293 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Tsallis Entropy ◽  
Complex Domain ◽  
Schwarz Function ◽  
Geometric Properties ◽  
Fractional Entropy ◽  
Euler Form

In this paper, we aim to introduce some geometric properties of analytic functions by utilizing the concept of fractional entropy in a complex domain. We extend the fractional entropy, type Tsallis entropy in the complex z-plane, by using some analytic functions. Established by this diffusion,we state specic new classes of analytic functions (type Schwarz function). Other geometric properties are validated in the sequel. Our development is completed by the Euler form Lemma and Jack Lemma.

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