Uniformly Close-to-Convex Functions with Respect to Conjugate Points

Syed Zakar Hussain Bukhari∗; Taimoor Salahuddin; Imtiaz Ahmad; Muhammad Ishaq; Shah Muhammad

doi:10.5666/KMJ.2022.62.2.229

Article

Kyungpook Mathematical Journal 2022; 62(2): 229-242

Published online June 30, 2022

Uniformly Close-to-Convex Functions with Respect to Conjugate Points

Syed Zakar Hussain Bukhari∗, Taimoor Salahuddin, Imtiaz Ahmad and Muhammad Ishaq, Shah Muhammad

Department of Mathematics, Mirpur University of Science and Technology(MUST), Mirpur-10250(AJK), Pakistan
e-mail : fatmi@must.edu.pk, taimoor_salahuddin@yahoo.com, drimtiaz.maths@must.edu.pk and ishaq_381@yahoo.com

Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
e-mail : shah.maths@must.edu.pk

Received: April 3, 2018; Revised: November 29, 2018; Accepted: December 19, 2018

Abstract

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Abstract

In this paper, we introduce a new subclass of k-uniformly close-to-convex functions with respect to conjugate points. We study characterization, coefficient estimates, distortion bounds, extreme points and radii problems for this class. We also discuss integral means inequality with the extremal functions. Our findings may be related with the previously known results.

Keywords: Characterizations, coefficients estimates, distortion bounds, extreme points, radii problems