scholarly journals Generalized Levinson's inequality and exponential convexity

2015 ◽  
Vol 35 (3) ◽  
pp. 397 ◽  
Author(s):  
Josip Pečarić ◽  
Marjan Praljak ◽  
Alfred Witkowski
Keyword(s):  
Exponential Convexity ◽  
Levinson’S Inequality

ON LEVINSON'S INEQUALITY

1989 ◽  
Vol 15 (2) ◽  
pp. 710 ◽  
Author(s):  
Pečarić
Keyword(s):  
Levinson’S Inequality

scholarly journals Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 797-813
Author(s):  
SAJID IQBAL ◽  
◽  
GHULAM FARID ◽  
JOSIP PEČARIĆ ◽  
ARTION KASHURI
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this paper we present variety of Hardy-type inequalities and their refinements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modified extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

Multidimensional reversed Hardy type inequalities for monotone functions

2014 ◽  
Vol 07 (04) ◽  
pp. 1450055
Author(s):  
Saad Ihsan Butt ◽  
Josip Pečarić ◽  
Ivan Perić ◽  
Marjan Praljak
Keyword(s):  
Mean Value ◽  
Monotone Functions ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Multidimensional Generalization ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Cauchy Means

In this paper, we will give some multidimensional generalization of reversed Hardy type inequalities for monotone functions. Moreover, we will give n-exponential convexity, exponential convexity and related results for some functionals obtained from the differences of these inequalities. At the end we will give mean value theorems and Cauchy means for these functionals.

scholarly journals Some mappings related to Levinson’s inequality for Hilbert space operators

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1995-2009 ◽  
Author(s):  
Jadranka Micic ◽  
Josip Pecaric
Keyword(s):  
Hilbert Space ◽  
Operator Inequality ◽  
Jensen Inequality ◽  
Hilbert Space Operators ◽  
Levinson’S Inequality

We observe properties of some mappings related to the Davis-Choi-Jensen inequality for Hilbert space operators. Using these results, we observe properties of some mappings related to Levinson?s operator inequality. Consequently, we obtain several refinements for each of these inequalities.

Radius of exponential convexity of certain subclass of analytic functions

2020 ◽  
Vol 29 (1) ◽  
pp. 109-112
Author(s):  
S. SUNIL VARMA ◽  
THOMAS ROSY ◽  
U. VADIVELAN
Keyword(s):  
Analytic Functions ◽  
Exponential Convexity

EXPONENTIAL CONVEXITY FOR DIVIDED DIFFERENCES RELATED TO HERMITE–HADAMARD INEQUALITIES

2012 ◽  
Vol 05 (04) ◽  
pp. 1250056
Author(s):  
Z. Pavić ◽  
J. Pečarić ◽  
A. Vukelić
Keyword(s):  
Convex Functions ◽  
Monotonicity Property ◽  
Divided Differences ◽  
Exponential Convexity ◽  
Exponentially Convex Functions

In this paper we obtain means which involve divided differences for n-convex functions. We examine their monotonicity property using exponentially convex functions.

scholarly journals Exponential convexity of Petrović and related functional

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
Saad I Butt ◽  
Josip Pečarić ◽  
Atiq Ur Rehman
Keyword(s):  
Exponential Convexity

scholarly journals Superadditivity, Monotonicity, and Exponential Convexity of the Petrović-Type Functionals

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Saad Ihsan Butt ◽  
Mario Krnić ◽  
Josip Pečarić
Keyword(s):  
Exponential Convexity ◽  
Monotonicity Properties

We consider functionals derived from Petrović-type inequalities and establish their superadditivity, subadditivity, and monotonicity properties on the corresponding realn-tuples. By virtue of established results we also define some related functionals and investigate their properties regarding exponential convexity. Finally, the general results are then applied to some particular settings.

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