Two-dimensional Laguerre planes over convex functions

1987 ◽  
Vol 23 (1) ◽  
Author(s):  
Rainer L�wen ◽  
Ulrike Pf�ller
Keyword(s):  
Convex Functions ◽  
Two Dimensional ◽  
Laguerre Planes

Two-Dimensional Trapezium Inequalities via pq-Convex Functions

2020 ◽  
pp. 21-34
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Themistocles M. Rassias
Keyword(s):  
Convex Functions ◽  
Two Dimensional

Two Dimensional Harmonic Quasi Convex Functions and Integral Inequalities

2018 ◽  
Vol 12 (6) ◽  
pp. 1203-1207
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Two Dimensional

scholarly journals Refined bounds of the quantum quadratures within the class of distance-disturbed convex functions in two dimensions

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 825-836
Author(s):  
Gabriela Cristescu ◽  
Muhammad Awan ◽  
Mihail Găianu
Keyword(s):  
Finite Elements ◽  
Convex Functions ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Convexity Properties

In this paper, we introduce the class of disturbed convex functions defined by means of distance perturbations in two dimensions on co-ordinates. Some quantum trapezoidal estimations are obtained for functions having two dimensional distance-disturbed convexity properties. Refined bounds of the quantum integrals of distance-disturbed convex functions on coordinates are deduced by using the rectangular finite elements technique. These approximations are as best as possible from the sharpness point of view. The sharpness of few results from the literature follows as consequence of the new results in this paper.

scholarly journals Approximately two-dimensional harmonic $(p_{1},h_{1})$-$(p_{2},h_{2})$-convex functions and related integral inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Artion Kashuri ◽  
Muhammad Nadeem ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Two Dimensional ◽  
New Class ◽  
Special Cases ◽  
Related Integral ◽  
Harmonic Convex

Abstract The aim of this study is to introduce the notion of two-dimensional approximately harmonic $(p_{1},h_{1})$ ( p 1 , h 1 ) -$(p_{2},h_{2})$ ( p 2 , h 2 ) -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic $(p_{1},h_{1})$ ( p 1 , h 1 ) -$(p_{2},h_{2})$ ( p 2 , h 2 ) -convex functions. We discuss in detail the special cases that can be deduced from the main results of the paper.

A FAMILY OF TWO-DIMENSIONAL LAGUERRE PLANES OF KLEINEWILLINGHÖFER TYPE II.A.2

2018 ◽  
Vol 105 (3) ◽  
pp. 366-379
Author(s):  
GÜNTER F. STEINKE
Keyword(s):  
Two Dimensional ◽  
Transitive Groups ◽  
Laguerre Planes ◽  
Translation Type ◽  
Central Automorphisms ◽  
Existence Question ◽  
Kleinewillinghöfer Type

Kleinewillinghöfer classified Laguerre planes with respect to linearly transitive groups of central automorphisms. Polster and Steinke investigated two-dimensional Laguerre planes and their so-called Kleinewillinghöfer types. For some of the feasible types the existence question remained open. We provide examples of such planes of type II.A.2, which are based on certain two-dimensional Laguerre planes of translation type. With these models only one type, I.A.2, is left for which no two-dimensional Laguerre planes are known yet.

scholarly journals Integral inequalities for two-dimensional pq-convex functions

Filomat ◽  
2016 ◽  
Vol 30 (2) ◽  
pp. 343-351
Author(s):  
Muhammad Noor ◽  
Muhammad Awan ◽  
Khalida Noor
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Two Dimensional
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