scholarly journals On some characterizations of sub-b-s-convex functions

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3885-3895 ◽  
Author(s):  
Jiagen Liao ◽  
Tingsong Du
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Generalized Convex Functions ◽  
Basic Properties ◽  
New Class ◽  
Constrained Programming

A new class of generalized convex functions called sub-b-s-convex functions is defined by modulating the definitions of s-convex functions and sub-b-convex functions. Similarly, a new class sub-bs-convex sets, which are generalizations of s-convex sets and sub-b-convex sets, is introduced. Furthermore, some basic properties of sub-b-s-convex functions in both general case and differentiable case are presented. In addition the sufficient conditions of optimality for both unconstrained and inequality constrained programming are established and proved under the sub-b-s-convexity.

scholarly journals Continued fractions built from convex sets and convex functions

2015 ◽  
Vol 17 (05) ◽  
pp. 1550003 ◽  
Author(s):  
Ilya Molchanov
Keyword(s):  
Convex Functions ◽  
Continued Fractions ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Ordered Semigroup ◽  
Minkowski Addition ◽  
Partially Ordered ◽  
The Family ◽  
Sufficient Conditions For Convergence

In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalization of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

scholarly journals Generalized Preinvex Functions and Their Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 493 ◽  
Author(s):  
Adem Kiliçman ◽  
Wedad Saleh
Keyword(s):  
Sufficient Conditions ◽  
Basic Properties ◽  
Preinvex Functions ◽  
Constrained Programming ◽  
New Inequalities

A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality constrained programming are discussed under the sub-b-s-preinvexity. Moreover, some new inequalities of the Hermite—Hadamard type for differentiable sub-b-s-preinvex functions are presented. Examples of applications of these inequalities are shown.

ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES

2012 ◽  
Vol 20 (01) ◽  
pp. 1-20 ◽  
Author(s):  
HUA-WEN LIU
Keyword(s):  
Classical Logic ◽  
Functional Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Triangular Norms ◽  
Basic Properties ◽  
New Class ◽  
Fuzzy Implications ◽  
Necessary And Sufficient

A new class of fuzzy implications, called (g, min )-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g, min )-implications are really a new class different from the known ( S , N )-, R -, QL - and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms ( t -norms) and triangular conorms ( t -conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.

scholarly journals Generalization of Quasi Convex Functions using Convolution

2020 ◽  
pp. 155-168
Author(s):  
Khalida Inayat Noor ◽  
Samar Abbas ◽  
Bushra Kanwal
Keyword(s):  
Convex Functions ◽  
Basic Properties ◽  
New Class ◽  
Inclusion Relations

In this paper, an up-to-date generalization of the class $\mathtt{C^\star}$ of quasi-convex functions is given by introducing new class $\mathfrak{\mathtt{C}^\star_g[a, b]}$. Furthermore its basic properties, its relationship with other subclasses of $\mathtt{S}$, inclusion relations and some other interesting properties are derived.

scholarly journals Strongly Reciprocally p-Convex Functions and Some Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Hao Li ◽  
Muhammad Shoaib Saleem ◽  
Ijaz Hussain ◽  
Muhammad Imran
Keyword(s):  
Convex Functions ◽  
Basic Properties ◽  
New Class

In this paper, we generalize the concept of strong and reciprocal convexity. Some basic properties and results will be presented for the new class of strongly reciprocally p-convex functions. Furthermore, we will discuss the Hermite–Hadamard-type, Jensen-type, and Fejér-type inequalities for the strongly reciprocally p-convex functions.

scholarly journals A Class of SemilocalE-Preinvex Functions and Its Applications in Nonlinear Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hehua Jiao ◽  
Sanyang Liu ◽  
Xinying Pai
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions ◽  
Convex Set ◽  
Basic Properties ◽  
New Class ◽  
Duality Results ◽  
Invex Set ◽  
Preinvex Functions ◽  
Class Of Functions

A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

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