SUFFICIENT CONDITIONS FOR CONVEX
FUNCTIONS OF ORDER γ
Muthaiyan Elumalai
Saveetha School of Engineering
SIMATS, Chennai - 602 105
Tamilnadu, INDIA

Abstract


Abstract. Sufficient conditions for functions to be starlike of order γ have been studied by authors Ramesha et al. and Nunokawa et al. Sufficient conditions for convexity involving higher order derivatives were investigated by Silverman. Taking ideas from the works of many authors we obtain interesting sufficient conditions for functions involving higher order derivatives to be univalently convex of order γ (0 ≤ γ < 1), using a well known best result in function theory and obtain as a special case, conditions of sufficiency for convexity if they belong to Am and A := A1.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 4
Year: 2018

DOI: 10.12732/ijam.v31i4.5

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