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) |
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. |