


Paper's Title:
On Generalization of Hardytype Inequalities
Author(s):
K. Rauf, S. Ponnusamy and J. O. Omolehin
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
krauf@unilorin.edu.ng
Department of Mathematics,
Indian Institute of Technology Madras,
Chennai 600 036,
India
samy@iitm.ac.in
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
omolehin_joseph@yahoo.com
Abstract:
This paper is devoted to some new generalization of Hardytype integral inequalities and the reversed forms. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. Improvement of some inequalities are also presented.
Paper's Title:
New Implicit KirkType Schemes for General Class of QuasiContractive Operators in Generalized Convex Metric Spaces
Author(s):
K. Rauf, O. T. Wahab and A. Ali
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
Email: krauf@unilorin.edu.ng
Department of Statistics and Mathematical
Sciences,
Kwara State University, Malete,
Nigeria.
Department of Mathematics,
Mirpur University of Science and Technology, Mirpur,
Pakistan.
Abstract:
In this paper, we introduce some new implicit Kirktype iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasicontractive type operators. The strong convergence, Tstability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.
Paper's Title:
HermiteHadamard Type Inequalities for kRiemann Liouville Fractional Integrals Via Two Kinds of Convexity
Author(s):
R. Hussain^{1}, A. Ali^{2}, G. Gulshan^{3}, A. Latif^{4} and K. Rauf^{5}
^{1,2,3,4}Department
of Mathematics,
Mirpur University of Science and Technology, Mirpur.
Pakistan.
Email^{1}:
rashida12@gmail.com
Email^{2}:
unigraz2009@yahoo.com
Email^{3}:
ghazalagulshan@yahoo.com
Email^{4}:
asialatif87@gmail.com
^{5}Department
of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
Email^{5}:
krauf@unilorin.edu.ng
Abstract:
In this article, a fundamental integral identity including the first order derivative of a given function via kRiemannLiouville fractional integral is established. This is used to obtain further HermiteHadamard type inequalities involving leftsided and rightsided kRiemannLiouville fractional integrals for mconvex and (s,m)convex functions respectively.
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