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    An application of salagean operator concerning starlike functions
    (MDPI, 2022) Güney, Hatun Özlem; Oros, Georgia Irina; Owa, Shigeyoshi
    As an application of the well-known Salagean differential operator, a new operator is introduced and, using this, a new class of functions S-n(alpha) is defined, which has the classes of starlike and convex functions of order alpha as special cases. Original results related to the newly defined class are obtained using the renowned Jack-Miller-Mocanu lemma. A relevant example is given regarding the applications of a new proven result concerning interesting properties of class S-n (alpha).
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    Öğe
    Introduction in third-order fuzzy differential subordination
    (Hacettepe Univ, Fac Sci, 2024) Oros, Georgia Irina; Oros, Gheorghe; Gueney, Hatun oezlem
    In light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination. Second-order fuzzy differential sub ordinations were taken into consideration for studies up until this point. The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by Jos & eacute; A. Antonino and Sanford S. Miller and still being investigated by scholars today. The key concepts and preliminary findings required for the development of this branch of fuzzy differential subordination are introduced. The class of admissible functions is specified, the fundamental theorems are established and the fundamental concepts of the third-order fuzzy subordination approach are presented. Several examples constructed as applications of the new results demonstrate the applicability of the new findings.
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    Öğe
    Introduction in third-order fuzzy differential subordination
    (Hacettepe University, 2024) Oros, Georgia Irina; Oros, Gheorghe; Güney, Özlem
    In light of the well-established and widely-used theory of differential subordination, recent works incorporating fuzzy elements into Geometric Function Theory have given rise to the concept of fuzzy differential subordination. Second-order fuzzy differential subordinations were taken into consideration for studies up until this point. The research described in this paper aims to expand the concept of fuzzy differential subordination to third-order fuzzy differential subordination, building on an idea first put forth in 2011 by Jos\'{e} A. Antonino and Sanford S. Miller and still being investigated by scholars today. The key concepts and preliminary findings required for the development of this branch of fuzzy differential subordination are introduced. The class of admissible functions is specified, the fundamental theorems are established and the fundamental concepts of the third-order fuzzy subordination approach are presented. Several examples constructed as applications of the new results demonstrate the applicability of the new findings.
  • [ X ]
    Öğe
    Relations of Harmonic Starlike Function Subclasses with Mittag-Leffler Function
    (Mdpi, 2024) Tasar, Naci; Sakar, Fethiye Muge; Aydogan, Seher Melike; Oros, Georgia Irina
    In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag-Leffler function. The investigation reveals inclusion relations concerning harmonic gamma-uniformly starlike mappings in the open unit disc, harmonic starlike functions and harmonic convex functions, highlighting the improvements given by the results presented here on previously published outcomes.
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    Toeplitz determinants for a certain family of analytic functions endowed with borel distribution
    (MDPI, 2023) Wanas, Abbas Kareem; Sakar, Fethiye Müge; Oros, Georgia Irina; Cotîrlă, Luminiţa-Ioana
    In this work, we derive coefficient bounds for the symmetric Toeplitz matrices (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.), which are the known first four determinants for a new family of analytic functions with Borel distribution series in the open unit disk U. Further, some special cases of results obtained are also pointed.