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YAŞAR, ELİF

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    Publication
    Convolutions of a subclass of harmonic univalent mappings
    (Türk Dünyası Matematik Topluluğu, 2020-01-01) Yaşar, Elif; Özdemir, Özge; YAŞAR, ELİF; ÖZDEMİR, ÖZGE; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi; 0000-0003-0176-4961; AAG-8247-2021; JGU-1442-2023
    The main object of this paper is to investigate the convolution of a subclass of harmonic univalent mappings which is denoted by f(a) and generalized harmonic univalent mapping which is denoted by P-c. We obtained P-c * f(a) is univalent and convex in the horizantal direction for 0 < c <= 2(1-a)/1+a. In addition, we present an example and illustrate it graphically with the help of Maple to explain the behaviour of image domain.
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    On convolutions of slanted half-plane mappings
    (Taylor, 2021-01-01) Yaşar, Elif; YAŞAR, ELİF; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-0176-4961; AAG-8247-2021
    The convolution of convex harmonic univalent functions in the unit disk, unlike analytic functions, may not be convex or even univalent. The main purpose of this work is to develop previous work involving the convolution of convex harmonic functions. Briefly, we obtain under which conditions the convolution of a right half-plane harmonic mapping having a dilatation -z and a slanted half-plane harmonic mapping with beta having a dilatation e(i mu)rho+z/1+rho z (|rho| < 1 and mu is an element of R) is univalent and convex in the direction -beta. We also provide an example illustrating graphically with the help of Maple to illuminate the result.
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    Close-to-convexity of a class of harmonic mappings defined by a third-order differential inequality
    (Tubitak Scientific & Technological Research Council Turkey, 2021) Yaşar, Elif; Yalçın, Sibel; YAŞAR, ELİF; YALÇIN TOKGÖZ, SİBEL; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-0176-4961; 0000-0002-0243-8263; AAG-8247-2021; AAE-9745-2020
    In this paper, we consider a class of normalized harmonic functions in the unit disk satisfying a third-order differential inequality and we investigate several properties of this class such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution. Moreover, as an application, we construct harmonic polynomials involving Gaussian hypergeometric function which belong to the considered class. We also provide examples illustrating graphically with the help of Maple.
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    Publication
    Convolutions of harmonic mappings convex in the horizontal direction
    (Hindawi, 2021-09-06) Çakmak, Serkan; Yaşar Elif; Yalçın Sibel; YAŞAR, ELİF; Çakmak, Serkan; Yalçın Sibel; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-0176-4961; 0000-0002-0243-8263; 0000-0003-0368-7672; GZG-2072-2022; AAG-8247-2021; AAE-9745-2020
    In this paper, we establish some results concerning the convolutions of harmonic mappings convex in the horizontal direction with harmonic vertical strip mappings. Furthermore, we provide examples illustrated graphically with the help of Maple to illuminate the results.