TY  - JOUR
T1  - MONOTONICITY RESULTS AND ASSOCIATED INEQUALITIES FOR  K-GAMMA FUNCTION
AU  - Ege, İnci
AU  - Yıldırım, Emrah
PY  - 2019
DA  - January
DO  - 10.18038/aubtda.438249
JF  - Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
JO  - Estuscience - Se
PB  - Eskisehir Technical University
WT  - DergiPark
SN  - 2667-4211
SP  - 104
EP  - 111
VL  - 20
IS  - 1
LA  - en
AB  - In this work, we find-analogue of Gautschi inequality and obtain some monotonicity results for-gamma function. By the aid of these, we also get some more inequalities.This study is inspired bythe work of Neumann in 2011. In the study, weestablish some double inequalities involving the ratio𝛤𝑘(𝑛+𝑠)𝛤𝑘(𝑛+𝑘), where 𝛤𝑘is the 𝑘-analogue of Euler’s gamma function. Some monotonicity results involvingk-gamma functionare found. By the aid of these results, some inequalitiessuchas[Γ𝑘(𝑘+𝜎)]𝑘𝜎≤∑[Γ𝑘(𝑘+𝑥𝑖)]𝑘𝑥𝑖𝑛𝑖=1for 𝑥𝑖>0, 1≤𝑖≤𝑛, where 𝜎=𝑥1+𝑥2+⋯+𝑥𝑛are valid.
KW  - Gamma function
KW  - k-gamma function
KW  - monotonicity
CR  - Gautschi W. Some elementary inequalities relating to the gamma and incomplete gamma function. Journal of Mathematics and Physics 1959; 38-1: 77-81.
CR  - Neuman E. Some inequalities for the gamma function. Appl. Math. Comput. 2011; 218-8: 4349-4352.
CR  - Diaz R, Pariguan E. On hypergeometric functions and Pachhammer k-symbol. Divulg. Mat. 2007; 15-2: 179-192.
CR  - Krasniqi V. Inequalities and monotonicity for the ration of k -gamma function. Scientia Magna. 2010; 6-1: 40-45.
CR  - Gradshteyn, I. S., Ryzhik, I. M. Table of integrals, series, and products. Academic Press, 2014.
UR  - https://doi.org/10.18038/aubtda.438249
L1  - https://dergipark.org.tr/en/download/article-file/710913
ER  -