Muhammad Ghaffar Khan

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All published works

Action	Title	Year	Authors
+ PDF Chat	Subclasses of q-Uniformly Starlike Functions Obtained via the q-Carlson–Shaffer Operator	2024	Qiuxia Hu Rizwan Salim Badar Muhammad Ghaffar Khan
+	Sharp Coefficient Bounds for a Class of Symmetric Starlike Functions Involving the Balloon Shape Domain	2024	Bilal Khan Jianhua Gong Muhammad Ghaffar Khan Fairouz Tchier
+ PDF Chat	Generalized Bounded Turning Functions Connected with Gregory Coefficients	2024	Huo Tang Zeeshan Mujahid Nazar Khan Fairouz Tchier Muhammad Ghaffar Khan
+	A class of analytic functions associated with sine hyperbolic functions	2024	S. Sivaprasad Kumar Muhammad Ghaffar Khan Bakhtiar Ahmad Wali Khan Mashwani
+ PDF Chat	Some properties of a class of holomorphic functions associated with tangent function	2024	Muhammad Ghaffar Khan Wali Khan Mashwani Zabidin Salleh Fairouz Tchier Bilal Khan Sarfraz Nawaz Malik
+	Sufficiency criteria for a class of convex functions connected with tangent function	2024	Muhammad Ghaffar Khan Sheza M. El-Deeb Daniel Breaz Wali Khan Mashwani Bakhtiar Ahmad
+	Sharp estimate for starlikeness related to a tangent domain	2024	Mohammad Faisal Khan Jong‐Suk Ro Muhammad Ghaffar Khan
+	Sharp inequalities for $ q $-starlike functions associated with differential subordination and $ q $-calculus	2024	Jianhua Gong Muhammad Ghaffar Khan Hala Alaqad Bilal Khan
+ PDF Chat	Applications of First-Order Differential Subordination for Subfamilies of Analytic Functions Related to Symmetric Image Domains	2023	Muhammad Ghaffar Khan Bilal Khan Jianhua Gong Fairouz Tchier Ferdous M. O. Tawfiq
+ PDF Chat	Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution	2023	Bilal Khan Muhammad Ghaffar Khan Timilehin Gideon Shaba
+ PDF Chat	Zalcman Functional and Majorization Results for Certain Subfamilies of Holomorphic Functions	2023	Muhammad Ghaffar Khan Bilal Khan Ferdous M. O. Tawfiq Jong‐Suk Ro
+	Subclasses of bi-univalent functions subordinate to gegenbauer polynomials	2023	Ala Amourah Zabidin Salleh B. A. Frasin Muhammad Ghaffar Khan Bakhtiar Ahmad
+ PDF Chat	Applications of q-Hermite Polynomials to Subclasses of Analytic and Bi-Univalent Functions	2022	Caihuan Zhang Bilal Khan Timilehin Gideon Shaba Jong‐Suk Ro Serkan Aracı Muhammad Ghaffar Khan
+ PDF Chat	Third Hankel Determinant for the Logarithmic Coefficients of Starlike Functions Associated with Sine Function	2022	Bilal Khan Ibtisam Aldawish Serkan Aracı Muhammad Ghaffar Khan
+ PDF Chat	Applications of Borel-Type Distributions Series to a Class of Janowski-Type Analytic Functions	2022	Bakhtiar Ahmad Muhammad Ghaffar Khan Luminiţa-Ioana Cotîrlă
+ PDF Chat	A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator	2022	Bakhtiar Ahmad Wali Khan Mashwani Serkan Aracı Saima Mustafa Muhammad Ghaffar Khan Bilal Khan
+	Applications of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>q</mi> </math>-Derivative Operator to the Subclass of Bi-Univalent Functions Involving <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>q</mi> </math>-Chebyshev Polynomials	2022	Bilal Khan Zhiguo Liu Timilehin Gideon Shaba Serkan Aracı Nazar Khan Muhammad Ghaffar Khan
+ PDF Chat	An Application of Fuzzy Multiple Linear Regression in Biological Paradigm	2022	Saima Mustafa Shumaila Ghaffar Murrium Bibi Muhammad Ghaffar Khan Qaisara Praveen Harish Garg Mahamane Saminou
+ PDF Chat	Fourth Hankel Determinant for a Subclass of Starlike Functions Based on Modified Sigmoid	2021	Wali Khan Mashwani Bakhtiar Ahmad Nazar Khan Muhammad Ghaffar Khan Sama Arjika Bilal Khan Ronnason Chinram
+	Coefficient functionals for a class of bounded turning functions related to modified sigmoid function	2021	Muhammad Ghaffar Khan Nak Eun Cho Timilehin Gideon Shaba Bakhtiar Ahmad Wali Khan Mashwani
+ PDF Chat	Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain	2021	Lei Shi H. M. Srivastava Muhammad Ghaffar Khan Nazar Khan Bakhtiar Ahmad Bilal Khan Wali Khan Mashwani
+ PDF Chat	Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions	2021	Lei Shi Bakhtiar Ahmad Nazar Khan Muhammad Ghaffar Khan Serkan Aracı Wali Khan Mashwani Bilal Khan
+ PDF Chat	Certain Coefficient Estimate Problems for Three-Leaf-Type Starlike Functions	2021	Lei Shi Muhammad Ghaffar Khan Bakhtiar Ahmad Wali Khan Mashwani Praveen Agarwal Shaher Momani
+ PDF Chat	Pascu-Type Analytic Functions by Using Mittag-Leffler Functions in Janowski Domain	2021	Wali Khan Mashwan Bakhtiar Ahmad Muhammad Ghaffar Khan Saima Mustafa Sama Arjika Bilal Khan
+ PDF Chat	Applications of Mittag-Leffer Type Poisson Distribution to a Subclass of Analytic Functions Involving Conic-Type Regions	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad Nazar Khan Wali Khan Mashwani Sama Arjika Bilal Khan Ronnason Chinram
+ PDF Chat	Applications of Some Generalized Janowski Meromorphic Multivalent Functions	2021	Bakhtiar Ahmad Muhammad Ghaffar Khan Maslina Darus Wali Khan Mashwani Muhammad Arif
+ PDF Chat	A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences	2021	Qiuxia Hu H. M. Srivastava Bakhtiar Ahmad Nazar Khan Muhammad Ghaffar Khan Wali Khan Mashwani Bilal Khan
+ PDF Chat	Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad G. Murugusundaramoorthy Wali Khan Mashwani Sibel Yalçın Timilehin Gideon Shaba Zabidin Salleh
+ PDF Chat	Applications of a New <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>q</mi> </math>-Difference Operator in Janowski-Type Meromorphic Convex Functions	2021	Bakhtiar Ahmad Muhammad Ghaffar Khan M. K. Aouf Wali Khan Mashwani Zabidin Salleh Huo Tang
+ PDF Chat	Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad Wali Khan Mashwani Timilehin Gideon Shaba Muhammad Arif
+	On subclasses of harmonic mappings involving Frasin operator	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad Zabidin Salleh Iing Lukman
+ PDF Chat	New classes of harmonic meromorphic multivalent starlike functions in Janowski domain	2021	Timilehin Gideon Shaba Bakhtiar Ahmad Muhammad Ghaffar Khan Zabidin Salleh Wali Khan Mashwani Shahid Khan
+ PDF Chat	Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad Janusz Sokół Muhammad Zubair Aslam Wali Khan Mashwani Ronnason Chinram Pattarawan Petchkaew
+ PDF Chat	On Janowski Type Harmonic Meromorphic Functions with respect to Symmetric Point	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad Maslina Darus Wali Khan Mashwani Shahid Khan
+	On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain	2021	Bakhtiar Ahmad Muhammad Ghaffar Khan B. A. Frasin M. K. Aouf Thabet Abdeljawad Wali Khan Mashwani Muhammad Arif
+ PDF Chat	On q-analogue of Janowski-type starlike functions with respect to symmetric points	2021	Muhammad Ghaffar Khan Bakhtiar Ahmad Raees Ahmad Khan Muhammad Zubair Zabidin Salleh
+ PDF Chat	Applications of Modified Sigmoid Functions to a Class of Starlike Functions	2020	Muhammad Ghaffar Khan Bakhtiar Ahmad G. Murugusundaramoorthy Ronnason Chinram Wali Khan Mashwani
+ PDF Chat	On Janowski Analytic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:math>-Starlike Functions in Symmetric Circular Domain	2020	Muhammad Ghaffar Khan Bakhtiar Ahmad B. A. Frasin Thabet Abdeljawad
+ PDF Chat	Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function	2020	Saeed Islam Muhammad Ghaffar Khan Bakhtiar Ahmad Muhammad Arif Ronnason Chinram
+ PDF Chat	Some Geometric Properties of a Family of Analytic Functions Involving a Generalized q-Operator	2020	Lei Shi Muhammad Ghaffar Khan Bakhtiar Ahmad
+	Applications of a differential operator to a class of harmonic mappings defined by Mittag-leffer functions	2020	Muhammad Ghaffar Khan Bakhtiar Ahmad Thabet Abdeljawad
+	A Class of Analytic Functions associated with Sine Hyperbolic Functions	2020	S. Sivaprasad Kumar Muhammad Ghaffar Khan Bakhtiar Ahmad Wali Khan Mashwani
+ PDF Chat	Meromorphic Starlike Functions with Respect to Symmetric Points	2020	Muhammad Ghaffar Khan Maslina Darus Bakhtiar Ahmad G. Murugusundaramoorthy Raees Ahmad Khan Nasir Khan

Common Coauthors

Coauthor	Papers Together
Bakhtiar Ahmad	30
Wali Khan Mashwani	21
Bilal Khan	16
Zabidin Salleh	7
Timilehin Gideon Shaba	7
Nazar Khan	7
Serkan Aracı	5
Ronnason Chinram	5
Fairouz Tchier	4
Lei Shi	4
Muhammad Arif	4
Thabet Abdeljawad	3
G. Murugusundaramoorthy	3
Maslina Darus	3
Sama Arjika	3
B. A. Frasin	3
Saima Mustafa	3
Jong‐Suk Ro	3
Jianhua Gong	3
Raees Ahmad Khan	2
S. Sivaprasad Kumar	2
Shahid Khan	2
Ferdous M. O. Tawfiq	2
Huo Tang	2
M. K. Aouf	2
Qiuxia Hu	2
H. M. Srivástava	2
Wali Khan Mashwan	1
Caihuan Zhang	1
Hala Alaqad	1
Sibel Yalçın	1
Mohammad Faisal Khan	1
Ibtisam Aldawish	1
Rizwan Salim Badar	1
Shaher Momani	1
Pattarawan Petchkaew	1
Zeeshan Mujahid	1
Mahamane Saminou	1
Sheza M. El-Deeb	1
Daniel Breaz	1
Shumaila Ghaffar	1
Iing Lukman	1
Luminiţa-Ioana Cotîrlă	1
Ala Amourah	1
Zhiguo Liu	1
Muhammad Zubair Aslam	1
Murrium Bibi	1
Nasir Khan	1
Sarfraz Nawaz Malik	1
Saeed Islam	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Radius Problems for Starlike Functions Associated with the Sine Function	2018	N. E. Cho Virendra Kumar S. Sivaprasad Kumar V. Ravichandran	17
+ PDF Chat	A coefficient inequality for certain classes of analytic functions	1969	F. R. Keogh E. P. Merkes	17
+ PDF Chat	Some class of analytic functions related to conic domains	2014	S. Kanas Dorina Răducanu	15
+ PDF Chat	Some Geometric Properties of a Family of Analytic Functions Involving a Generalized q-Operator	2020	Lei Shi Muhammad Ghaffar Khan Bakhtiar Ahmad	14
+ PDF Chat	Extremal problems for a family of functions with positive real part and for some related families	1970	W. Janowski	14
+	On a Subclass of Strongly Starlike Functions Associated with Exponential Function	2014	Rajni Mendiratta Sumit Nagpal V. Ravichandran	13
+	Hankel determinant of order three for familiar subsets of analytic functions related with sine function	2019	Muhammad Arif Mohsan Raza Huo Tang Shehzad Hussain Hassan Khan	12
+	Bound for the fifth coefficient of certain starlike functions	2015	V. Ravichandran Shelly Verma	12
+	Operators of Basic (or q-) Calculus and Fractional q-Calculus and Their Applications in Geometric Function Theory of Complex Analysis	2020	H. M. Srivastava	11
+	Starlike functions associated with a cardioid	2015	Kanika Sharma Naveen Kumar Jain V. Ravichandran	11
+ PDF Chat	Coefficient estimates of new classes of q-starlike and q-convex functions of complex order	2016	T. M. Seoudy M. K. Aouf	10
+ PDF Chat	A proof of the Bieberbach conjecture	1985	Louis de Branges	9
+	Certain Class of Starlike Functions Associated with Modified Sigmoid Function	2019	Priyanka Goel S. Sivaprasad Kumar	9
+	Starlike Functions Associated with Cosine Functions	2020	Khadija Bano Mohsan Raza	9
+	Bounds for the second Hankel determinant of certain bi-univalent functions	2016	Halit Orhan N. Magesh Jagadeesan Yamini	9
+ PDF Chat	Applications of Modified Sigmoid Functions to a Class of Starlike Functions	2020	Muhammad Ghaffar Khan Bakhtiar Ahmad G. Murugusundaramoorthy Ronnason Chinram Wali Khan Mashwani	9
+	On a class of starlike functions related to a shell-like curve connected with Fibonacci numbers	2012	Jacek Dziok Ravinder Krishna Raina Janusz Sokół	8
+ PDF Chat	A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences	2021	Qiuxia Hu H. M. Srivastava Bakhtiar Ahmad Nazar Khan Muhammad Ghaffar Khan Wali Khan Mashwani Bilal Khan	8
+	Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function	2021	H. M. Srivastava Bilal Khan Nazar Khan Muhammad Tahir Sarfraz Ahmad Nasir Khan	7
+	XI.—On <i>q</i>-Functions and a certain Difference Operator	1909	F. H. Jackson	7
+ PDF Chat	GEOMETRIC AND APPROXIMATION PROPERTIES OF GENERALIZED SINGULAR INTEGRALS IN THE UNIT DISK	2006	George A. Anastassiou Sorin G. Gal	7
+ PDF Chat	Starlike Functions Related to the Bell Numbers	2019	Nak Eun Cho Sushil Kumar Virendra Kumar V. Ravichandran H. M. Srivastava	7
+	On the Hankel determinants of univalent functions	1967	Christian Pommerenke	7
+ PDF Chat	Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions	2021	Lei Shi Bakhtiar Ahmad Nazar Khan Muhammad Ghaffar Khan Serkan Aracı Wali Khan Mashwani Bilal Khan	6
+	Coefficient inequality for a function whose derivative has a positive real part	2006	Aini Janteng Suzeini Abdul Halim Maslina Darus	6
+	On the Coefficients of Subordinate Functions	1945	W. W. Rogosinski	6
+	On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain	2021	Bakhtiar Ahmad Muhammad Ghaffar Khan B. A. Frasin M. K. Aouf Thabet Abdeljawad Wali Khan Mashwani Muhammad Arif	6
+	Eine Bemerkung Über Ungerade Schlichte Funktionen	1933	M. Fekete Gábor Szegő	6
+ PDF Chat	A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives	2020	Bilal Khan Zhi-Guo Liu H. M. Srivastava Nazar Khan Maslina Darus Muhammad Tahir	6
+	A generalization of starlike functions	1990	Mourad E. H. Ismail E. P. Merkes D. Styer	6
+	On $H_3(1)$ Hankel determinant for some classes of univalent functions	2009	K. O. Babalola	6
+ PDF Chat	Third Hankel Determinants for Subclasses of Univalent Functions	2016	Paweł Zaprawa	6
+ PDF Chat	Some extremal problems for certain families of analytic functions I	1973	W. Janowski	6
+ PDF Chat	On a certain univalent mapping.	1959	Kôichi Sakaguchi	6
+	On the Second Hankel Determinant of Areally Mean p-Valent Functions	1976	J. W. Noonan D. K. Thomas	6
+ PDF Chat	Generalized q-Baskakov operators	2011	Ali Aral Vijay Gupta	5
+ PDF Chat	Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli	2013	Mohsan Raza Sarfraz Nawaz Malik	5
+	Radius problems in the class	2009	Janusz Sokół	5
+ PDF Chat	Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain	2021	Lei Shi H. M. Srivastava Muhammad Ghaffar Khan Nazar Khan Bakhtiar Ahmad Bilal Khan Wali Khan Mashwani	5
+	Second Hankel determinant for the class of Bazilevic functions	2015	D. Vamshee Krishna T. RamReddy	5
+	On the Zalcman conjecture for starlike and typically real functions	1986	Johnny E. Brown Anna Tsao	5
+ PDF Chat	Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function	2020	Saeed Islam Muhammad Ghaffar Khan Bakhtiar Ahmad Muhammad Arif Ronnason Chinram	5
+ PDF Chat	Early coefficients of the inverse of a regular convex function	1982	Richard J. Libera Eligiusz J. Złotkiewicz	5
+ PDF Chat	Starlike and Convex Functions Associated with a Nephroid Domain	2020	Lateef Ahmad Wani A. Swaminathan	5
+	Applications of higher-order <i>q</i>-derivatives to the subclass of <i>q</i>-starlike functions associated with the Janowski functions	2020	Muhammad Sabil Ur Rehman Qazi Zahoor Ahmad H. M. Srivastava Nazar Khan Maslina Darus Bilal Khan	5
+	On the Second Hankel Determinant of Mean Univalent Functions	1968	W. K. Hayman	5
+	New subfamily of meromorphic multivalent starlike functions in circular domain involving <i> <sub>q-</sub> </i>differential operator	2018	Muhammad Arif Bakhtiar Ahmad	5
+ PDF Chat	Bounds for the second Hankel determinant of certain univalent functions	2013	See Keong Lee V. Ravichandran Shamani Supramaniam	5
+ PDF Chat	On the second Hankel determinant of areally mean 𝑝-valent functions	1976	J. W. Noonan Derek K. Thomas	5
+ PDF Chat	DIFFERENTIAL SUBORDINATION FOR FUNCTIONS ASSOCIATED WITH THE LEMNISCATE OF BERNOULLI	2012	Rosihan M. Ali Nak Eun Cho V. Ravichandran S. Sivaprasad Kumar	5