


Paper's Title:
Scope of the Logarithmic Mean
Author(s):
Murali Rao and Agnish Dey
Department of Mathematics,
University of Florida,
1400 Stadium Road, Gainesville,
Florida 32611,
U. S. A.
Email: mrao@ufl.edu
URL: http://people.clas.ufl.edu/mrao
Email: agnish@ufl.edu
URL: http://people.clas.ufl.edu/agnish
Abstract:
A number a is between two numbers x and y if and only if a is a convex combination of x and y, in other words, it is a "weighted mean" of x and y. Geometric mean, arithmetic mean are well known examples of these "means". Of more recent vintage is the logarithmic mean which has been considered in many articles in the literature. In this note, we first discuss some of its properties. Then we shall introduce the L function and explore the inverse of this function and its connection with the Lambert's Omega function.
Paper's Title:
Some New Inequalities of HermiteHadamard and Fejér Type for Certain Functions with Higher Convexity
Author(s):
Steven G. From
Department of Mathematics,
University of Nebraska at Omaha,
Omaha, Nebraska 681820243,
U.S.A.
Email: sfrom@unomaha.edu
Abstract:
In this paper, we present some new inequalities of HermiteHadamard or Fejér
type for certain functions satisfying some higher convexity conditions on one or
more derivatives.
An open problem is given also.
Some applications to the logarithmic mean are given.
Paper's Title:
Convergence Speed of Some Random ImplicitKirktype Iterations for Contractivetype Random Operators
Author(s):
H. Akewe, K.S. Eke
Department of Mathematics,
Covenant University,
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
Email: hudson.akewe@covenantuniversity.edu.ng,
kanayo.eke@covenantuniversity.edu.ng
Abstract:
The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicitKirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractivetype random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.
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