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ON CERTAIN GENERALIZED q-INTEGRAL OPERATORS OF ANALYTIC FUNCTIONS

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In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p- valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

Abstract

In this article, we first consider a linear multiplier fractional q-differintegral operator and then use it to define new subclasses of p- valent analytic functions in the open unit disk U. An attempt has also been made to obtain two new q-integral operators and study their sufficient conditions on some classes of analytic functions. We also point out that the operators and classes presented here, being of general character, are easily reducible to yield many diverse new and known operators and function classes.

참고문헌 (24)

  1. J.W. Alexander, "Functions which map the interior of the unit circle upon simple regions", Ann. of Math. (2), 17(1), pp.12~22 (1915)
  2. F. M. Al-Oboudi, "On univalent functions defined by a generalized S˘al˘agean operator", Int. J. Math. Math. Sci, 2004(25-28), pp.1429~1436 (2004)
  3. D. Breaz, "Some properties for integral operators on some analytic functions with complex order", Acta Math. Acad. Paedagog. Nyh´azi. (N.S.), 25(1), pp.39~43 (2009)
  4. D. Breaz, "Two integral operators", Studia Univ. Babe¸s-Bolyai Math, 47(3), pp.13~19 (2002)
  5. D. Breaz, "The integral operator on the classes S∗α(b) and Cα(b)", J. Math. Inequal, 2(1), pp.97~100 (2008)
  6. D. Breaz, "A new general integral operator", Tamsui Oxf. J. Math. Sci, 25(4), pp.407~414 (2009)
  7. D. Breaz, "A new integral univalent operator", Acta Univ. Apulensis Math. Inform, (16), pp.11~16 (2008)
  8. S. Bulut, "A note on the paper of Breaz and G¨uney", J. Math. Inequal, 2(4), pp.549~553 (2008)
  9. P. N. Chichra, "Regular functions f(z) for which zf′(z) is α-spiral-like", Proc. Amer. Math. Soc, 49, pp.151~160 (1975)
  10. B. A. Frasin, "Family of analytic functions of complex order", Acta Math. Acad. Paedagog. Nyh´azi. (N.S.), 22(2), pp.179~191 (2006)
  11. B. A. Frasin, "Convexity of integral operators of p-valent functions", Math. Comput. Modelling, 51(5-6), pp.601~605 (2010)
  12. G. Gasper, "Basic hypergeometric series" (1990), Cambridge Univ. Press
  13. R. J. Libera, "Univalent α-spiral functions", Canad. J. Math, 19, pp.449~456 (1967)
  14. M. A. Nasr, "Starlike function of complex order", J. Natur. Sci. Math, 25(1), pp.1~12 (1985)
  15. V. Pescar, "Sufficient conditions for univalence of certain integral operators", Indian J. Math, 42(3), pp.347~351 (2000)
  16. J. A. Pfaltzgraff, "Univalence of the integral of f′(z)λ", Bull. London Math. Soc, 7(3), pp.254~256 (1975)
  17. S. D. Purohit, "A new class of multivalently analytic functions associated with fractional q-calculus operators", Fract. Differ. Calc, 2(2), pp.129~138 (2012)
  18. S. D. Purohit, "Certain subclasses of analytic functions associated with fractional q-calculus operators", Math. Scand, 109(1), pp.55~70 (2011)
  19. S. D. Purohit, "Fractional q-calculus and certain subclass of univalent analytic functions", Mathematica, 55(78)(1), pp.62~74 (2013)
  20. S. D. Purohit, "Some classes of analytic and multivalent functions associated with q-derivative operators", Acta Univ. Sapientiae Math, 6(1), pp.5~23 (2014)
  21. S. D. Purohit, "On a subclass of p-valent analytic functions involving fractional q-calculus operators", Kuwait J. Sci, 42(1), pp.1~15 (2015)
  22. G. S¸. S˘al˘agean, "Subclasses of univalent functions, in Complex analysisfifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981)", Lecture Notes in Math, 1013, pp.362~372 (1983), Springer
  23. K. A. Selvakumaran, "Convexity of certain q-integral operators of p-valent functions", Abstr. Appl. Anal, 2014, pp.7~ (2014)
  24. P. Wiatrowski, "The coefficients of a certain family of holomorphic functions", Zeszyty Nauk. Uniw. L´odz. Nauki Mat. Przyrod. Ser. II, (39 Mat), pp.75~85 (1971)

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