BiographyDhananjay Gopal has a doctorate in Mathematics from Guru Ghasidas University, Bilaspur, India and currently Assistant Professor of Applied Mathematics in S. V. National Institute of Technology Surat, Gujarat, India. He is author and co-author of several papers in journals and proceedings. He is devoted to general research on the theory of Non linear Analysis and fuzzy metric fixed point.
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
• Fixed point theory,
• Non-linear analysis,
• Fuzzy analysis
• Image processing
Singing and Poetry
Published: Jan 03, 2018 by Applied Mathematics and Computation
Authors: D Gopal, M Abbas C Vetro
We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an a-type contractive mapping and then for a generalized b-type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results.
Published: Jan 03, 2016 by International Journal of General Systems
Authors: S Shukla, D Gopal, AF Roldán-López-de-Hierro
In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.
Published: Jan 03, 2016 by Mathematical Modelling and Analysis
Authors: S Shukla, D Gopal, R Rodríguez-López
In this paper, we introduce a new class of operators called fuzzy-Presic- Ciric operators. For this type of operators, the existence and uniqueness of fixed point in M-complete fuzzy metric spaces endowed with H-type t-norms are established.
Published: Jan 03, 2016 by Acta Mathematica Scientia
Authors: D Gopal, M Abbas, DK Patel, C Vetro
In this paper, we introduce new concepts of alpha-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from -GF-contractions given in . Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space.