scholarly journals Stability of the Prékopa-Leindler inequality for log-concave functions

2021 ◽  
Vol 386 ◽  
pp. 107810
Author(s):  
Károly J. Böröczky ◽  
Apratim De
Keyword(s):  
Concave Functions

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Integral Inequality ◽  
Target Function ◽  
Convexity Property ◽  
Concave Functions ◽  
Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

scholarly journals Quantitative combinatorial geometry for concave functions

2021 ◽  
Vol 182 ◽  
pp. 105465
Author(s):  
Sherry Sarkar ◽  
Alexander Xue ◽  
Pablo Soberón
Keyword(s):  
Combinatorial Geometry ◽  
Concave Functions

Log-Concave Functions And Poset Probabilities

COMBINATORICA ◽  
1998 ◽  
Vol 18 (1) ◽  
pp. 85-99 ◽  
Author(s):  
Jeff Kahn ◽  
Yang Yu
Keyword(s):  
Concave Functions

Some Properties of Generalized Concave Functions

1973 ◽  
Vol 21 (1) ◽  
pp. 305-313 ◽  
Author(s):  
W. A. Thompson ◽  
Darrel W. Parke
Keyword(s):  
Concave Functions

scholarly journals A NOTE ON INTEGRAL INEQUALITIES OF HADAMARD TYPE FOR LOG-CONVEX AND LOG-CONCAVE FUNCTIONS

2012 ◽  
Vol 16 (2) ◽  
pp. 479-496 ◽  
Author(s):  
Gou-Sheng Yang ◽  
Kuei-Lin Tseng ◽  
Hung-Ta Wang
Keyword(s):  
Integral Inequalities ◽  
Concave Functions

scholarly journals Weak Orlicz–Hardy martingale spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550062 ◽  
Author(s):  
Yong Jiao ◽  
Lian Wu ◽  
Lihua Peng
Keyword(s):  
Atomic Decomposition ◽  
Type Inequality ◽  
Sublinear Operator ◽  
Sufficient Condition ◽  
Concave Functions ◽  
Atomic Decompositions ◽  
Stochastic Basis ◽  
Decomposition Theorems

In this paper, several weak Orlicz–Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient condition for a sublinear operator defined on the weak Orlicz–Hardy martingale spaces to be bounded is given. Further, we investigate the duality of weak Orlicz–Hardy martingale spaces and obtain a new John–Nirenberg type inequality when the stochastic basis is regular. These results can be regarded as weak versions of the Orlicz–Hardy martingale spaces due to Miyamoto, Nakai and Sadasue.

scholarly journals New inequalities of Hermite-Hadamard type for n-times differentiable convex and concave functions with applications

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2609-2621
Author(s):  
M.A. Latif ◽  
S.S. Dragomir
Keyword(s):  
Concave Functions ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
Special Means ◽  
Second Derivatives ◽  
Special Cases ◽  
New Inequalities

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide refinements of some results already exist in literature. Applications to trapezoidal formula and special means of established results are given.

Sign in / Sign up

Export Citation Format

Share Document