PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2015 | 13 | 1 |
Tytuł artykułu

Third-order differential subordination and superordination involving a fractional operator

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-08
zaakceptowano
2015-09-09
online
2015-10-23
Twórcy
  • Faculty of Computer Science and Information Technology, University Malaya, 50603
    Kuala Lumpur, Malaysia
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia,
    E-mail: mzaini@unimap.edu.my
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia,
    E-mail: mzaini@unimap.edu.my
Bibliografia
  • [1] Alexander J. W., Functions which map the interior of the unit circle upon simple regions, Ann. of Math., 1915, 17, 12–22.[Crossref]
  • [2] Libera R. J., Some classes of regular univalent functions, Proc. Amer. Math. Soc., 1965, 16, 755–758.[Crossref]
  • [3] Bernardi S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 1969, 135, 429–446.
  • [4] Miller S. S., Mocanu P. T., Reade M. O., Starlike integral operators, Pacific J. Math., 1978, 79, 157–168.
  • [5] Miller S. S., Mocanu P. T., Classes of univalent integral operators, J. Math. Anal. Appl., 1991, 157, 147–165.[Crossref]
  • [6] Singh R., On Bazilevic functions, Proc. Amer. Math. Soc., 1973, 18 261–271.
  • [7] Pascu N. N., Pescar V., On integral operators of Kim-Merkes and Pfaltz-graff, Mathematica (Cluj), 1990, 2, 185–192.
  • [8] Pescar V., Breaz D., Some integral operators and their univalence, Acta Univ. Apulensis Math., Inform. 2008, 15, 147–152.
  • [9] Breaz D., Breaz N., Srivastava H. M., An extension of the univalent condition for a family of integral operators, Appl. Math. Lett.,(2009), 22, 41–44.[WoS][Crossref]
  • [10] Breaz D., Darus M., Breaz N., Recent Studies on Univalent Integral Operators, Alba Iulia: Aeternitas, 2010.
  • [11] Darus M., Ibrahim R. W., On subclasses of uniformly Bazilevic type functions involving generalized differential and integraloperators, FJMS, 2009, 33, 401–411.
  • [12] Darus M., Ibrahim R. W., On inclusion properties of generalized integral operator involving Noor integral, FJMS, 2009, 33,309–321.
  • [13] Hernandez R., Prescribing the preschwarzian in several complex variables, Annales Academiae Scientiarum FennicaeMathematica, 2011, 36, 331–340.[Crossref][WoS]
  • [14] Ong K. W., Tan S. L., Tu Y. E., Integral operators and univalent functions, Tamkang Journal of Mathematics, 2012, 43(2),215–221.
  • [15] Goluzin G. M., On the majorization principle in function theory (Russian). Dokl. Akad. Nauk. SSSR, 1953, 42, 647–650.
  • [16] Suffridge T. J., Some remarks on convex maps of the unit disk. Duke Math. J., 1970, 37, 775–777.
  • [17] Robinson R. M., Univalent majorants, Trans. Amer. Math. Soc., 1947, 61, 1–35.[Crossref]
  • [18] Hallenbeck D. J., Ruscheweyh S., Subordination by convex functions, Proc. Amer. Math. Soc., 1975, 52, 191–195.[Crossref]
  • [19] Miller S.S., Mocanu P.T., Differential subordinations and univalent function, Michig. Math. J., 1981, 28, 157–171.[Crossref]
  • [20] Miller S.S., Mocanu P.T., Differential subordinations and inequalities in the complex plane, J. Diff. Eqn., 1987, 67, 199–211.
  • [21] Miller S.S., Mocanu P.T., The theory and applicatins of second-order differential subordinations, Studia Univ. Babes-Bolyai, math.,1989, 34, 3–33.
  • [22] Miller S. S., Mocanu P. T., Differential Subordinations, Theory and applications, Monographs and Textbooks in Pure and AppliedMathematics, 225, Dekker, New York, 2000.
  • [23] Miller S. S., Mocanu P. T., Subordinants of differetial superordinations, Complex Var. Theory Appl., 2003, 48, 815–826.
  • [24] Bulboac Ma T., Differential subordinations and superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca,2005.
  • [25] Baricz A., Deniz E., Caglar M., Orhan H., Differential subordinations involving the generalized Bessel functions, Bull. Malays.Math. Sci. Soc., DOI: 10.1007/s40840-014-0079-8.[WoS][Crossref]
  • [26] Cho N. E., Bilboaca T., Srivastava H. M., A general family of integral operators and associated subordination and superordinationproperties of some special analytic function classes, Appl. Math. Comput., 2012, 219, 2278–2288.[WoS]
  • [27] Kuroki K., Srivastava H. M., Owa S., Some applications of the principle of differential, Electron. J. Math. Anal. Appl., 2013, 1 (50),40–46.
  • [28] Xu Q.-H., Xiao H.-G., Srivastava H. M., Some applications of differential subordination and the Dziok-Srivastava convolutionoperator, Appl. Math. Comput., 2014, 230, 496–508.
  • [29] Ali R. M., Ravichandran V., Seenivasagan N., Differential subordination and superordination of analytic functions defined by theDziok-Srivastava operator, J. Franklin Inst., 2010, 347, 1762–1781.[WoS]
  • [30] Ali R. M., Ravichandran V., Seenivasagan N., On Subordination and superordination of the multiplier transformation formeromorphic functions, Bull. Malays. Math. Sci. Soc., 2010, 33, 311–324.
  • [31] Ponnusamy S., Juneja O. P., Third-order differential inequalities in the complex plane, Current Topics in Analytic Function Theory,World Scientific, Singapore, London, 1992.
  • [32] Antonion J. A., Miller S. S., Third-order differential inequalities and subordinations in the complex plane, Complex Var. TheoryAppl., 2011, 56, 439–454.
  • [33] Jeyaraman M. P., Suresh T. K., Third-order differential subordination of analysis functions, Acta Universitatis Apulensis, 2013, 35,187–202.
  • [34] Tang H., Srivastiva H. M., Li S., Ma L., Third-order differential subordinations and superordination results for meromorphicallymultivalent functions associated with the Liu-Srivastava Operator, Abstract and Applied Analysis, 2014, 1–11.[WoS][Crossref]
  • [35] Tang H., Deniz E., Third-order differential subordinations results for analytic functions involving the generalized Bessel functions,Acta Math. Sci., 2014, 6, 1707–1719.[WoS][Crossref]
  • [36] Tang H., Srivastiva H. M., Deniz E., Li S., Third-order differential superordination involving the generalized Bessel functions, Bull.Malays. Math. Sci. Soc., 2014, 1–22.[WoS]
  • [37] Farzana H. A., Stephen B. A., Jeyaraman M. P., Third-order differential subordination of analytic function defined by functionalderivative operator, Annals of the Alexandru Ioan Cuza University - Mathematics, 2014, 1–16.
  • [38] B. C. Carlson and D. B. Shaffer,Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 1984, 15, 737–745.
  • [39] Machado J. T., Discrete-time fractional-order controllers, Fractional Calculus and Applied Analysis, 2001, 4, 47–66.
  • [40] Pu Y.-F., Zhou J.-L., Yuan X., Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement,Image Processing, IEEE Transactions on, 2010, 19, 491–511.[WoS]
  • [41] Jalab H. A., Ibrahim R. W., Fractional Conway polynomials for image denoising with regularized fractional power parameters,J. Math. Imaging Vis., 2015, 51, 442–450.[Crossref][WoS]
  • [42] Jalab H A, Ibrahim R. W., Fractional Alexander polynomials for image denoising, Signal Processing, 2015, 107, 340–354.
  • [43] Wu G.C., Baleanu D., Zeng S.D., Deng Z.G., Discrete fractional diffusion equation, Nonlinear Dynamics, 2015, 80, 1–6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0068
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.