PARTIAL SUMS OF MITTAG-LEFFLER FUNCTION

Bansal D., ORHAN H.

JOURNAL OF MATHEMATICAL INEQUALITIES, cilt.12, sa.2, ss.423-431, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.7153/jmi-2018-12-31
  • Dergi Adı: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.423-431
  • Anahtar Kelimeler: Mittag-Leffler function, analytic function, univalent, subordination, NORMALIZED BESSEL-FUNCTIONS, GEOMETRIC-PROPERTIES, STARLIKENESS, CONVEXITY, UNIVALENCE, RADIUS, ORDER
  • Atatürk Üniversitesi Adresli: Evet

Özet

In the present investigation, Mittag-Leffler function with their normalization are con- sidered. In this paper, we will study the ratio of a function of the form (1.4) to its sequence of partial sums (E-lambda,E-mu)(n) (z) = z + Sigma(n)(k=1) Gamma(mu)/(Gamma(lambda k+mu) z(k+1 ) We will determine lower bounds for R {E-lambda,(mu)(z)/(E-lambda,(mu))(n)(z)}, R {(E-lambda,(mu))(n)(z)/E-lambda,(mu)(z)}, {E'(lambda,)(mu)(z)/(E'(lambda,)(mu))(n)(z)} and R {(E'(lambda,)(mu))(n)(z)/E'(lambda,)(mu)(z)} Results obtained are new and their usefulness are depicted by deducing several interesting examples.