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http://dx.doi.org/10.5831/HMJ.2019.41.4.745

INEQUALITIES OF EXTENDED (p, q)-BETA AND CONFLUENT HYPERGEOMETRIC FUNCTIONS  

Mubeen, Shahid (Department of Mathematics, University of Sargodha)
Nisar, Kottakkaran Sooppy (Department of Mathematics, College of Arts and Sciences)
Rahman, Gauhar (Department of Mathematics, Shaheed Benazir Bhutto University)
Arshad, Muhammad (Department of Mathematics, International Islamic University)
Publication Information
Honam Mathematical Journal / v.41, no.4, 2019 , pp. 745-756 More about this Journal
Abstract
In this paper, we establish the log convexity and Turán type inequalities of extended (p, q)-beta functions. Likewise, we present the log-convexity, the monotonicity and Turán type inequalities for extended (p, q)-confluent hypergeometric function by utilizing the inequalities of extended (p, q)-beta functions.
Keywords
Beta function; Extended hypergeometric functions; $Tur{\acute{a}}n$-type inequalities; log-convexity;
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1 R. P. Agarwal, N. Elezovic and J. Pecaric, On some inequalities for beta and gamma functions via some classical inequalities, J. Inequal. Appl., 2005(5)(2005), 593-613.
2 M. Biernacki and J. Krzyz, On the monotonicity of certain fractionals in the theory of analytic functions, Ann. Univ. Mariae Curie-Sklodowska. Sect. A., 9 (1955), 135-147.
3 S. Butt, J. Pecaric and A. Rehman, Exponential convexity of Petrovic and related functional, J. Inequal. Appl., 2011(2011), 89.   DOI
4 M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math., 55 (1994), 99-123.   DOI
5 M. A. Chaudhry, A. Qadir, M. Rafique and S. M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math., 78 (1997), 19-32.   DOI
6 M.A. Chaudhry, A. Qadir, H.M. Srivastava and R.B. Paris, Extended hypergeometric and con uent hypergeometric functions, Appl. Math. Comput. , 159 (2004), 589-602.   DOI
7 J. Choi, A. K. Rathie and R. K. Parmar, Extension of extended beta, hypergeometric and con uent hypergeometric functions, Honam Mathematical J., 36 (2014), 357-385.   DOI
8 S. S. Dragomir, R. P. Agarwal and N. S. Barnett, Inequalities for beta and gamma functions via some classical and new inequalities, J. Inequal. Appl., 5(2) (2000), 103-165.
9 P. Kumar, S. P. Singh and S. S. Dragomir, Some inequalities involving beta and gamma functions, Nonlinear Anal. Forum, 6(1)(2001), 143-150.
10 D. Karp and S. M. Sitnik, Log-convexity and log-concavity of hypergeometric-like function, J. Math. Anal. Appl., 364(2) (2010), 384-394.   DOI
11 D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht (1993).
12 S. R. Mondal, Inequalities of extended beta and extended hypergeometric functions, J. Inequal. Appl., (2017) 2017,10   DOI
13 W. Rudin, Real and Complex Analysis, 3rd edn. McGraw-Hill International Editions (1987).
14 P. Turan, On the zeros of the polynomials of Legendre, Casopis pro Pestovani Mat. a Fys, 75 (1950), 113-122.