JENSEN–MERCER INEQUALITY AND RELATED RESULTS IN THE FRACTAL SENSE WITH APPLICATIONS

Saad Ihsan Butt, Saba Yousaf (), Hijaz Ahmad and Taher A. Nofal ()
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Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus Pakistan
Saba Yousaf: Department of Mathematics, COMSATS University Islamabad, Lahore Campus Pakistan
Hijaz Ahmad: Section of Mathematics, International Telematic University, Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy3Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar 64001, Iraq
Taher A. Nofal: Department of Mathematics, College of Science Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-11

Abstract: The most notable inequality pertaining convex functions is Jensen’s inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen’s inequality called as Jensen–Mercer’s inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions. The purpose of this paper is to establish a generalized Jensen–Mercer inequality for a generalized convex function on a real linear fractal set ℠α (0 < α ≤ 1). Further, we also demonstrate some generalized Jensen–Mercer-type inequalities by employing local fractional calculus. Lastly, some applications related to Jensen–Mercer inequality and α-type special means are given. The present approach is efficient, reliable, and may motivate further research in this area.

Keywords: Jensen–Mercer Inequality; Fractal Space; Generalized Convex Function; Generalized Jensen Inequality; Local Fractional Derivative; Local Fractional Integral (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0218348X22400084

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