Some Properties and Inequalities for a Two-Parameter Generalization of the Incomplete Exponential Integral Function

Ahmed Yakubu *

Department of Mathematics, Faculty of Physical Sciences, University for Development Studies, Nyankpala Campus, P. O. Box TL1350, Tamale, N/R, Ghana.

Bashiru Abubakari

Department of Mathematics Education, Faculty of Education, University for Development Studies, Main Campus, Tamale, N/R, Ghana.

Francis Kwaku Assan

Department of Mathematics, Akrokeri College of Education, Obuasi, A/R, Ghana.

*Author to whom correspondence should be addressed.


Abstract

Motivated by the p-analogue of the exponential integral function [1], we introduce a two-parameter generalization of the Incomplete Exponential Integral function. By using the classical H¨older’s and Young’s inequalities, among other analytical techniques, we establish some new inequalities involving the generalized function.

Keywords: Two-parameter Generalization of the incomplete exponential integral function, Holder’s inequality and Young’s inequality for scalars.


How to Cite

Yakubu, A., Abubakari, B., & Assan, F. K. (2023). Some Properties and Inequalities for a Two-Parameter Generalization of the Incomplete Exponential Integral Function. Asian Research Journal of Mathematics, 19(10), 154–160. https://doi.org/10.9734/arjom/2023/v19i10737

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References

Yakubu A, Nantomah K, Iddrisu MM. A p-Analogue of the Exponential Integral Function and Some Properties. Adv. Inequal. Appl. 2020;(2020):7:1-9.

Chiccoli C, Lorenzutta S, Maino G. Recent results for generalized exponential integrals. Comput. Math. Appl. 1989;19(5):21-29.

Sroysang B. Inequalities for the incomplete exponential integral function. Commun. Math. Appl. 2013;4(2):145-148. 159 Yakubu et al.; Asian Res. J. Math., vol. 19, no. 10, pp. 154-160, 2023; Article no.ARJOM.103863

Sroysang B. More on some inequalities for the incomplete exponential integral function. Mathematica Aeterna. 2014;(2):131-134.

Sulaiman WT. Turan inequalities of the exponential integral function. Commun. Optima. Theory. 2012;1:35- 41.

Yakubu A, Nantomah K, Iddrisu MM. The i-th Derivative of the p-Analogue of the exponential integral function and some properties. Journal of Mathematical and Computational Science. 2020;10(5):1801-1807.

Hunt GE. The transport equation of radiative transfer with axial symmetry. SI AMI. Appl. Math. 1968;16(1143):228-237.

Milgram MA. The generalized integro-exponential function. Math. Comp. 1985;(44):441-458.

Nantomah K, Merovci F, Nasiru S. A generalization of the exponential integral and some associated inequalities. Honan Math. J. 2017;39(1):49-59.

Salem A. A q-analogue of the exponential integral. Afr. Math. Un. Springer-Verlag. 2011;24:117-125.

Miller J, Hurst RP. Simplified calculation of the exponential integral. Office of Ordnance Research, S. Army. 1957;187-193.

Kaplan C. On some functions related to the exponential integrals. Aerospace Research Lab. ARL-70-0097;

Jameson GJO. Sine,cosine and exponential integrals. Math. Comput. 2015;99:276-289.

Nantomah K. Generalized Holder’s and Minkowski’s inequalities for Jackson’s q-integral and some applications to the incomplete q-gamma function. Abstr. Appl. Anal. 2017;6. Article ID 9796873.

Kazarinoff ND. Analytic inequalities, Holt, Rinehart and Winston, New York; 1961.

Mitrinovic DS. Analytic inequalities. Springer-Verlag, New York; 1970.

Monica MA, Nantomah K. Some inequalities for the Chaudhry-Zubair Extension of the gamma function. Asian Res. J. Math. 2019;14(1):1-9.