D. Gopal’s research focuses on algebraic/topological fixed point theory and fuzzy analysis with possible applications in solving differential and integral equations along with utilizing the fuzzy analysis and related fixed point theorems in Optimization Theory, Quantum Mechanics and computer science.
Because of the diverse applications of fixed point theory, this theory has widely been applied in many other branches of science and engineering. These facts motivated us to work on this topic. Our aim was to study the various problems of existence of fixed/common fixed point and iterative techniques which could provide a suitable frame work to study and solve various linear and non-linear operator equations. In pursuit of proposed studies, we have formulated and established some new results on fixed point/common fixed point theory and as applications of the obtained results; we established some existence results for the solution of Volterra type integral equation, fractional differential eaquations as well as for some type of no-linear integral equations. These results are published in the form of research papers in : Applied Mathematics and Computation 2014 (Elsevier), Banach Journal of Mathematical Analysis 2015, Acta Mathematica Scientia 2016 (Elsevier ), International Journal of General Systems 2016 (Taylor & Francis), Mathematical Modelling and Analysis 2016 (Taylor & Francis) and many other journals.
D. Gopal has active research collaborations with KMUTT, Bangkok, Thammasat University Bangkok and in his research pursuits he has visited South Africa, Tahiland, Japan and Iran.
Areas of Research / Professional Expertise
• Non-linear analysis,
• Fuzzy analysis
• Image processing