Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions [PDF]
Sahand Communications in Mathematical Analysis, 2022 We extend the definitions of $\nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $\int P(y)f(y) dy$ and $\int \int P(y,z) f(y,z) dy dz$ are deduced.
Faraz Mehmood, Asif Khan, Muhammad Adnan
doaj +1 more source
Quasi Semi and Pseudo Semi (p,E)-Convexity in Non-Linear Optimization Programming
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023 The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively.
Revan I. Hazim, Saba N. Majeed
doaj +1 more source
A comprehensive review of the Hermite-Hadamard inequality pertaining to fractional differential operators [PDF]
Surveys in Mathematics and its Applications, 2023 A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p ...
Muhammad Tariq +3 more
doaj
Hermite-Hadamard type inequalities for Wright-convex functions of several variables [PDF]
Opuscula Mathematica, 2015 We present Hermite-Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplices.
Dorota Śliwińska, Szymon Wąsowicz
doaj +1 more source
Mathematics, 2023 In the frame of fractional calculus, the term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus and objective of this review paper is to present Hermite–Hadamard (H-H)-type inequalities ...
Muhammad Tariq +2 more
doaj +1 more source
Ostrowski-Type Fractional Integral Inequalities: A Survey
Foundations, 2023 This paper presents an extensive review of some recent results on fractional Ostrowski-type inequalities associated with a variety of convexities and different kinds of fractional integrals.
Muhammad Tariq +2 more
doaj +1 more source
Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind.
Ali Hassan +3 more
doaj +1 more source
Continued fractions built from convex sets and convex functions [PDF]
, 2014 In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions with deterministic terms are provided.
Molchanov, Ilya
core +2 more sources
Compositions and Averages of Two Resolvents: Relative Geometry of Fixed Points Sets and a Partial Answer to a Question by C. Byrne [PDF]
, 2010 We show that the set of fixed points of the average of two resolvents can be found from the set of fixed points for compositions of two resolvents associated with scaled monotone operators.
Bauschke, Heinz H., Wang, Xianfu
core +1 more source
Modulus of convexity for operator convex functions [PDF]
, 2014 Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence.
Kim, Isaac H.
core +3 more sources