A NEW SUBCLASS OF ANALYTIC FUNCTIONS CONNECTED WITH GALUE-TYPE FUNCTION | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 2, 2025, Pages 1-12 PDF (206.79 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.317561.1128 | ||
| Authors | ||
| SHINDE VIHAR S* 1; Chavhan S.B2 | ||
| 1Department of Mathematics, K.N.B.A.C and V.P.S COLLEGE SOLAPUR, M.S, INDIA | ||
| 2D.B.A.C and S College, Bhokar, Dist. Nanded | ||
| Abstract | ||
| The Gauss-type function related to univalent functions typically refers to certain special functions that are closely connected to the theory of univalent (or schlicht) functions. Univalent functions are analytic functions that are injective (one-to-one) on a given domain, commonly the unit disk. One of the most notable examples in this context is the Gaussian function (often called the Gaussian or Gauss hypergeometric function), which is defined in terms of the hypergeometric series. However, this function is not usually directly related to univalent functions but is a special function in complex analysis and other areas. Special functions and their properties, including those related to Gauss-type functions, are used in various problems in number theory and algebraic geometry. For instance, modular forms, which have connections with hypergeometric functions, play a significant role in these fields. Gaussian functions are widely used in integral transforms, such as the Fourier and Laplace transforms, due to their mathematical properties and their role in solving various boundary value problems. Their properties are leveraged in solving differential equations, mapping and transformations, probability theory, and various applied fields. | ||
| Keywords | ||
| analytic; starlike coefficient estimate; error function; convolution | ||
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