A global optimality result using Geraghty type contraction

Authors

  • Binayak S. Choudhury Bengal Engineering and Science University, Shibpur
  • Pranati Maity Bengal Engineering and Science University, Shibpur
  • P. Konar Institute of Technology Marine Engineering, South 24 Pargana, West Bengal

DOI:

https://doi.org/10.11121/ijocta.01.2014.00184

Keywords:

Contraction, proximity point, metric space, global minima, fixed point.

Abstract

In this paper we prove two proximity point results for finding the distance between two sets. Unlike the best approximation theorems they provide with globally optimal values. Here our approach is to reduce the problem to that of finding optimal approximate solutions of some fixed point equations. We use Geraghty type contractive inequalities in our theorem. Two illustrative examples are given.

Author Biographies

Binayak S. Choudhury, Bengal Engineering and Science University, Shibpur

Dr.B.S.Choudhury is a Professor of Mathematics since 2003. He has supervised severalPh.D. students in different areas of pure and Applied Mathematics and Theoretical Physics and haspublished a good number of research articles ininternational journals. Particularly he has publishedmore than 100 research articles in metricspace related studies. He has served his institutein several administrative capacities.

Pranati Maity, Bengal Engineering and Science University, Shibpur

Pranati Maity received bachelor of science in Mathematics from Vidyashagar university in2005. She received her master degree in Mathematicsand bachelor of education from GuruGhasidas Viswavidyalaya in 2007 and 2009 respectively.She is going to submit Ph.D thesis.Her research interest is nonlinear analysis and optimization.

P. Konar, Institute of Technology Marine Engineering, South 24 Pargana, West Bengal

Pulak Konar completed his master degree in 2007 from Guru Ghasidas Viswavidyalaya, C.G,India. At present he is pursuing his Ph.D. Heis also working as an Assistant Professor in theDepartment of Mathematics in Institute of Tech-nology & Marine Engineering since 2009. His research interest is nonlinear analysis, functional analysis and topology.

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Published

2014-06-12

How to Cite

Choudhury, B. S., Maity, P., & Konar, P. (2014). A global optimality result using Geraghty type contraction. An International Journal of Optimization and Control: Theories &Amp; Applications (IJOCTA), 4(2), 99–104. https://doi.org/10.11121/ijocta.01.2014.00184

Issue

Section

Applied Mathematics & Control