The purpose of this paper is to study a generalization strongly $\eta$-convex functions using the fractal calculus developed by Yang \cite{Yang}, namely generalized function. Among other results, we obtain some Hermite-Hadamard and Fej\'er type inequalities for class functions.

We present an optimal gradient method for smooth strongly convex optimization. The is in the sense that its worst-case bound on distance to point exactly matches lower oracle complexity class of problems, meaning no black-box first-order can have a better guarantee without further assumptions problems at hand. In addition, we provide constructive recipe obtaining algorithmic parameters and illu...

Srivastava-Attiya operator is used to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk U . For each of these new function classes, several inclusion relationships are established. Some interesting corollaries and applications of the results presented here are also discussed. Mathematics subject classification (2000): 30C45...

A smooth, strongly $\mathbb{C}$-convex, real hypersurface $S$ in $\mathbb{CP}^n$ admits a projective dual CR structure addition to the standard structure. Given smooth function $u$ on $S$, we provide characterizations for when can be decomposed as sum of and function. Following work Lee pluriharmonic boundary values, characterization using differential forms. We further tangential vector fields...

A known family of fractional integral operators (with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk U. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesti...

The aim of this paper is to find a convenient and practical method to approximate a given real-valued function of multiple variables by linear operators, which approximate all strongly convex functions from above (or from below). Our main contribution is to use this additional knowledge to derive sharp error estimates for continuously differentiable functions with Lipschitz continuous gradients...