Duality for convolution on subclasses of analytic functions and weighted integral operators

• Autorzy: Amini Ebrahim , Fardi Mojtaba , Al-Omari Shrideh , Nonlaopon Kamsing

Identyfikatory

DOI

10.1515/dema-2022-0168

• Języki publikacji: EN

Abstrakty

EN

In this article, we investigate a class of analytic functions defined on the unit open disc U = {z : ∣z∣ < 1}, such that for every f ∈ Pα(β , γ), α > 0, 0 ≤ β ≤ 1, 0 < γ ≤ 1, and ∣z∣ < 1, the inequality Re (…) > 0 holds. We find conditions on the numbers α, β, and γ such that Pα (β, γ) ⊆ SP (λ), for λ ∈ (…), where SP (λ) denotes the set of all λ-spirallike functions. We also make use of Ruscheweyh’s duality theory to derive conditions on the numbers α, β, γ and the real-valued function φ so that the integral operator Vφ(f) maps the set Pα(β, γ) into the set SP (λ), provided φ is non-negative normalized function (…) and (…).

Słowa kluczowe

EN

convolution; Hadamard product; duality principle; λ-spirallike functions; dual set; Gaussian hypergeometric function

PL

splot; iloczyn; zasada dualności Hadamarda; funkcja gwiaździsta; funkcja hipergeometryczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220168
• Opis fizyczny: Bibliogr. 40 poz.

Twórcy

autor

Amini Ebrahim

• Department of Mathematics, Payme Noor University, P. O. Box 19395-4697, Tehran, Iran

autor

Fardi Mojtaba

• Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, P. O. Box 115, Shahrekord, Iran

autor

Al-Omari Shrideh

• Department of Scientific Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan

autor

Nonlaopon Kamsing

• Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Bibliografia

• [1] M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Jpn. Acad. Ser. A 69 (1993), 234–237. DOI: https://doi.org/10.3792/pjaa.69.234.
• [2] M. Nunokawa, O. S. Kwon, Y. J. Sim, and N. E. Cho, Sufficient conditions for Carathéodory functions, Filomat. 32 (2018), no. 3, 1097–1106. DOI: https://doi.org/10.1515/ms-2017-0290.
• [3] M. Nunokawa, and J. Sokol, New conditions for starlikeness and strongly starlikeness of order alpha, Houst. J. Math. 43 (2017), no. 2, 333–344.
• [4] M. Nunokawa, and J. Sokol, Some applications of first-order differential subordinations, Math. Slovaca 67, no. 4, 939–944, DOI: https://www.jstor.org/stable/24898719.
• [5] Q. Xu and S. Lu, The Alexander transformation of a subclass of spirallike functions of type β, J. Inequal. Pure Appl. Math. 10 (2009), no. 1, 1–17, DOI: https://doi.org/10.1007/s00025-018-0771-3.
• [6] M. Hussain, M. Raza, and J. Sokol, On a subclass of starlike functions, Results Math. 73 (2018), no. 22, 1–12, DOI: https://doi.org/10.1007/s00025-018-0771-3.
• [7] S. Ruscheweyh, Duality for Hadamard products with applications to extremal problems for functions regular in the unit disc, Trans. Amer. Math Soc. 210 (1975), 63–74. DOI: https://doi.org/10.2307/1997122.
• [8] S. Ruscheweyh, Convolutions in Geometric Function Theory, Sem. Math. Sup. vol. 83, Press Univ. Montreal, 1982.
• [9] Y. C. Kim and F. Ronning, Integral transforms of certain subclasses of analytic functions, Rocky Mountain J. Math. 24 (1994), no. 2, 529–538. DOI: https://doi.org/10.1006/jmaa.2000.7383.
• [10] S. S. Miller and P. T. Mocanu, Differential subordinations: theory and applications, Series of Monographs and Textbooks in Pure and Applied Mathematics, vol. 225, Marcel Dekker Inc., New York, 2000.
• [11] S. Ponnusamy and F. Ronning, Duality for Hadamard product applied to certain integral transforms, Complex Var. Theory Appl. 32 (1997), 263–287. DOI: https://doi.org/10.1080/17476939708814995.
• [12] S. Ponnusamy and F. Ronning, Integral transforms of a class of analytic functions, Complex var Theory Appl. 53 (2008), 423–434. DOI: https://doi.org/10.1080/17476930701685767.
• [13] H. Silverman, E. M. Silvia, and D. Telage, Convolutions conditions for convexity starlikeness and spiral-likeness, Math. Z. 162 (1978), no. 2, 125–130. DOI: https://doi.org/10.1007/BF01215069.
• [14] S. Al-Omari, D. Baleanu, and D. Purohit, Some results for Laplace-type integral operator in quantum calculus, Adv. Differ. Equ. 124 (2018), 1–10. DOI: https://doi.org/10.1186/s13662-018-1567-1.
• [15] S. Al-Omari, On q-analogues of Mangontarum transform of some polynomials and certain class of H-functions, Nonlinear Studies 23 (2016), no. 1, 51–61. DOI: https://doi.org/10.1016/j.jksus.2015.04.008.
• [16] S. Al-Omari, On q-analogues of the Mangontarum transform for certain q-Bessel functions and some application, J. King Saud Univ. Sci. 28 (2016), no. 4, 375–379. DOI: https://doi.org/10.1016/j.jksus.2015.04.008.
• [17] S. Al-Omari, q-analogues and properties of the Laplace-type integral operator in the quantum calculus theory, J. Ineq. Appl. 203 (2020), 1–14. DOI: https://doi.org/10.1186/s13660-020-02471-0.
• [18] S. Al-Omari, On a q-Laplace-type integral operator and certain class of series expansion, Math. Meth. Appl. Sci. 240 (2021), no. 10, 1–12. DOI: https://doi.org/10.1002/mma.6002.
• [19] S. Al-Omari, Estimates and properties of certain q-Mellin transform on generalized q-calculus theory, Adv. Difference Equ. 242 (2021), 1–11.
• [20] A. Abdeljawad, R. P. Agarwal, E. Karapinar, and P. S. Kumari, Solutions of the nonlinear integral equation and fractional differential equation using the technique of a fixed point with a numerical experiment in extended b-metric space, Symmetry 11 (2019), no. 686, 1–18, DOI: https://doi.org/10.3390/sym11050686.
• [21] B. Alqahtani, H. Aydi, E. Karapinar, and V. Rakocevic, A solution for Volterra fractional integral equations by hybrid contractions, Mathematics 7 (2019), no. 694, 1–10. DOI: https://doi.org/10.3390/math7080694.
• [22] E. Karapinar, T. Abdeljawad, and F. Jarad, Applying new fixed point theorems on fractional and ordinary differential equations, Adv. Difference Equ. 421 (2019), no. 2019, 1–25.
• [23] S. Chandak, D. L. Suthar, S. K. Al-Omari, and S. Gulyaz-Ozyurt, Estimates of classes of generalized special functions and their application in the fractional (k,s)-calculus theory, J. Func. Sp. 2021 (2021), 1–10, DOI: https://doi.org/10.1155/2021/9582879.
• [24] N. Khan, T. Usman, M. Aman, S. K. Q. Al-Omari and J. Choi, Integral transforms and probability distributions involving generalized hypergeometric function, Georg. J. Math. 28 (2021), no. 6, 1–12, DOI: https://doi.org/10.1515/gmj-2021-2105.
• [25] N. Khan, T. Usman, M. Aman, S. Al-Omari, and S. Araci, Computation of certain integral formulas involving generalized wright function, Adv. Difference Equ. 491 (2020), 1–11, DOI: https://doi.org/10.1186/s13662-020-02948-8.
• [26] S. Jain, P. Agarwal, B. Ahmad, and S. K. Q. Al-Omari, Certain recent fractional integral inequalities associated with the hypergeometric operators, J. King Saud Univ. Sci. 4 (2015), no. 17, 82–86, DOI: https://doi.org/10.1016/j.jksus.2015.04.002.
• [27] P. Agarwal, S. Jain, I. O. Kiymaz, M. Chand, and S. K. Q. AL-Omari, Certain sequences of functions involving generalized hypergeometric functions, Math. Scie. Appl. E-Notes 3 (2015), no. 2, 45–53, DOI: https://doi.org/10.36753/mathenot.421329.
• [28] Y. Xiao-Jun, A new integral transform with an application in heat-transfer problem, Thermal Science 20 (2016), no. 3, 677–681. DOI: https://doi.org/10.2298/TSCI16S3677Y.
• [29] S. Al-Omari, Hartley transforms on a certain space of generalized Functions, Georgian Math. J. 20 (2013), no. 30, 415–426. DOI: https://doi.org/10.1515/gmj-2013-0034.
• [30] X. Liang, Feng Gaoa, Ya-Nan Gao, Xiao-Jun Yang, Applications of a novel integral transform to partial differentialequations, J. Nonlinear Sci. Appl. 10 (2017), no. 2, 528–534. DOI: https://doi.org/10.22436/jnsa.010.02.18.
• [31] O. Ersoy, A comparative review of real and complex Fourier-related transforms, Proc. IEEE 82 (1994), no. 3, 429–447, DOI: https://doi.org/10.1109/5.272147.
• [32] X.-J. Yang, A new integral transform operator for solving the heat-diffusion problem, Appl. Math. Letters 64 (2017), 193–197, DOI: https://doi.org/10.1016/j.aml.2016.09.011.
• [33] P. K. Banerji, S. K. Al-Omari, and L. Debnath. Tempered distributional Fourier sine(cosine) transform, Integ. Trans. Spl. Funct. 17 (2006). no. 11, 759–768, DOI: https://doi.org/10.1080/10652460600856534.
• [34] A. H. Zemanian, Generalized Integral Transformation, Dover Publications, Inc., New York. First published by Interscience Publishers, New York, 1987.
• [35] S. K. Al-Omari and J. F. Al-Omari, Hartley transform for Lp Boehmians and spaces of ultradistributions, Int. Math. Forum 7 (2012), no. 9, 433–443.
• [36] R. Balasubramanian, S. Ponnusamy, and M. Vuorinen, On hypergeometric functions and function space, J. Comput. Appl. Math. 139 (2002), 299–322. DOI: https://doi.org/10.1016/S0377-0427(01)00417-4.
• [37] R. Balasubramanian, S. Ponnusamy, and D. J. Prabhakaran, Duality techniques for certain integral transforms to be starlike, J. Math. Anal. Appl. 293 (2004), 355–373. DOI: https://doi.org/10.1016/j.jmaa.2004.01.011.
• [38] I. Graham and G. Kohr, Geometric Function Theory in One and Higher Dimensions, Marcel Dekker, Inc, New York, 2003.
• [39] R. Fournier and S. Ruscheweyh, On two extremal problems related to univalent functions, Rocky Mountain J. Math. 24 (1994), no.2, 529–538. DOI: https://doi.org/10.1216/rmjm/1181072416.
• [40] L. E. Britvina, A class of integral transforms related to the Fourier cosine convolution, Integ. Trans. Spec. Funct. 16 (2005), no. 5, 379–389, DOI: https://doi.org/10.1080/10652460412331320395.