In this paper we prove some properties for functions that are multivalent in the unit disc |z| < 1 in the complex plane. As a corollary we obtain that if f(z) is p-valent, p ≥ 10, and |arg{f(p)(z)}|<π in |z| < 1, then f (z) is p-valent starlike. [ABSTRACT FROM AUTHOR]
The aim of the present paper is to introduce and study a subfamily of holomorphic and normalized functions defined by a differential inequality. Some geometric properties of this family of holomorphic functions and different problems of a family of such functions are presented. [ABSTRACT FROM AUTHOR]
In this paper, we would like to state well-known Ostrowski inequality via generalized Montgomery identity for the Φ - λ -convex function. Also, we would like to state the generalization of the classical Ostrowski inequality via generalized fractional integrals, which is obtained for functions whose first derivative in absolute values is Φ - λ -convex. Moreover we establish some Ostrowski type inequalities via generalized fractional integrals and their particular cases for the class of functions whose derivatives in absolute values at certain powers are Φ - λ - convex by using different techniques including Hölder's inequality and power mean inequality. Also, standard results would be capture as special cases. Moreover, some applications in terms of special means would also be given. [ABSTRACT FROM AUTHOR]
For positive numbers t, p,q,c and an analytic function f(z) in an annulus R1 < |z| < R2, let Mt,ϕ,q,c(f,r) be the area integral means of f with respect to the weighted area measure ϕ' (|z| q)|z| q−2 dA(z), where R1 ≤ c < R2 . We show that Mt,ϕ,q,c(f,r) 1/p is a convex function of r if f and ϕ satisfy certain conditions. The convexities of logMt,ϕ,q,c(f,r) in r and log r can be obtained as special cases. [ABSTRACT FROM AUTHOR]
We derive two new fractional quantum integral identities. Using these identities we obtain several new fractional quantum estimates of trapezoid like inequalities essentially using the class of preinvex functions. [ABSTRACT FROM AUTHOR]