scholarly journals Exponentially Convex Functions on Hypercomplex Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Buthinah A. Bin Dehaish
Keyword(s):  
Convex Functions ◽  
Natural Generalization ◽  
Hypercomplex System ◽  
Exponentially Convex Functions ◽  
Definition Of ◽  
Structure Measure

A hypercomplex system (h.c.s.)L1(Q,m)is, roughly speaking, a space which is defined by a structure measure(c(A,B,r),(A,B∈ℬ(Q))), such space has been studied by Berezanskii and Krein. Our main result is to define the exponentially convex functions (e.c.f.) on (h.c.s.), and we will study their properties. The definition of such functions is a natural generalization of that defined on semigroup.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

Refinements of the majorization-type inequalities via green and fink identities and related results

2018 ◽  
Vol 68 (4) ◽  
pp. 773-788 ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić ◽  
Ana Vukelić
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Ostrowski’S Inequality ◽  
New Family ◽  
Exponentially Convex Functions ◽  
The Difference

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

scholarly journals Hermite-Hadamard Type Inequalities Associated with Coordinated((s,m),QC)-Convex Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yu-Mei Bai ◽  
Shan-He Wu ◽  
Ying Wu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Definition Of

In this paper, we introduce the definition of coordinated((s,m),QC)-convex function and establish some Hermite-Hadamard type integral inequalities for coordinated((s,m),QC)-convex functions.

A note on recursive functions

1996 ◽  
Vol 6 (2) ◽  
pp. 127-139 ◽  
Author(s):  
Nicoletta Sabadini ◽  
Sebastiano Vigna ◽  
Robert F. C. Walters
Keyword(s):  
Programming Language ◽  
Concurrent Programming ◽  
Natural Generalization ◽  
Computational Power ◽  
Recursive Functions ◽  
Definition Of ◽  
Computable Functions

In this paper, we propose a new and elegant definition of the class of recursive functions, which is analogous to Kleene's definition but differs in the primitives taken, thus demonstrating the computational power of the concurrent programming language introduced in Walters (1991), Walters (1992) and Khalil and Walters (1993).The definition can be immediately rephrased for any distributive graph in a countably extensive category with products, thus allowing a wide, natural generalization of computable functions.

scholarly journals New Hermite-Hadamard type inequalities for exponentially convex functions and applications

2020 ◽  
Vol 5 (6) ◽  
pp. 6874-6901 ◽  
Author(s):  
Shuang-Shuang Zhou ◽  
◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Convex Functions ◽  
Exponentially Convex Functions

scholarly journals On Presupposition Projection with Trivalent Connectives

2019 ◽  
Vol 29 ◽  
pp. 582
Author(s):  
Yoad Winter
Keyword(s):  
Natural Generalization ◽  
Projection Algorithm ◽  
Presupposition Projection ◽  
Definition Of ◽  
As Effects

A basic puzzle about presuppositions concerns their projection from propositional constructions. This problem has regained much attention in the last decade since many of its prominent accounts, including variants of the trivalent Strong Kleene connectives, suffer from the so-called *proviso problem*.This paper argues that basic insights of the Strong Kleene system can be used without invoking the proviso problem. It is shown that the notion of *determinant value* that underlies the definition of the Strong Kleene connectives leads to a natural generalization of the filtering conditions proposed in Karttunen's article ``Presuppositions of compound sentences'' (LI, 1973). Incorporating this generalized  condition into an incremental projection algorithm avoids the proviso problem as well as the derivation of conditional presuppositions. It is argued that the same effects that were previously modelled using conditional presuppositions may be viewed as effects of presupposition suspension and contextual inference on presupposition projection.

scholarly journals Operator (p, η)-Convexity and Some Classical Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Chuanjun Zhang ◽  
Muhammad Shoaib Saleem ◽  
Waqas Nazeer ◽  
Naqash Shoukat ◽  
Yongsheng Rao
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Generalized Function ◽  
Basic Properties ◽  
Definition Of

In this paper, we will introduce the definition of operator p,η-convex functions, we will derive some basic properties for operator p,η-convex function, and also check the conditions under which operations’ function preserves the operator p,η-convexity. Furthermore, we develop famous Hermite–Hadamard, Jensen type, Schur type, and Fejér’s type inequalities for this generalized function.

scholarly journals Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 807 ◽  
Author(s):  
Saima Rashid ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Order Derivative ◽  
Fundamental Identity ◽  
First Order ◽  
Special Means ◽  
Exponentially Convex Functions ◽  
New Inequalities

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

Sign in / Sign up

Export Citation Format

Share Document