Dr. DEBASIS SHARMA

Dr. Debasis Sharma received his Ph.D. in Mathematics from IIIT Bhubaneswar and his M.Sc. in Mathematics from NIT Rourkela. He is currently serving as an Assistant Professor at Model Degree College, Rayagada, under the Higher Education Department, Government of Odisha. His research interests include Numerical Functional Analysis, Iterative Methods for Nonlinear Operator Equations, Convergence Analysis, and Computational Mathematics.
Dr. Sharma has published more than 30 research articles in reputed international journals. His research primarily focuses on the development, analysis, and implementation of efficient numerical methods for solving nonlinear problems arising in applied mathematics, science, and engineering. He is actively engaged in advancing computational techniques with an emphasis on accuracy, convergence, and practical applicability.

EDUCATION

Ph.D. in Mathematics

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics, Analysis, Numerical Analysis, Computational Mathematics

Scopus Publications

Expansion of Convergence Domain of a Parameter-Based Iteration Scheme for Equations in Banach Spaces
Eulalia Martínez, Debasis Sharma
Symmetry, 2025
The performance of iterative schemes used to solve nonlinear operator equations is strongly influenced by the initial guess. Therefore, it is essential to accurately determine convergence radii and develop theoretical strategies to broaden the region where convergence is guaranteed in order to enhance the reliability and efficiency of these methods. A crucial tool for this purpose is local convergence analysis, which investigates behavior near the true solution to establish convergence criteria. This work is dedicated to extending the convergence region of a parameter-based iteration scheme of the fifth-order. We carry out a comprehensive local convergence study within the framework of Banach spaces and derive precise formulas for the convergence radius, error estimates, and convergence zones associated with the method. A notable advantage of our approach is that it relies solely on the first derivative and avoids the need for additional conditions, making it easier to apply and significantly expanding the convergence region relative to earlier approaches. The theoretical contributions are further validated through a series of numerical experiments applied to diverse classes of nonlinear equations. Furthermore, the examination of the basins of attraction and their symmetry provides a deeper understanding of the method’s dynamic characteristics, robustness, and effectiveness in tackling complex-valued polynomial equations.
Extended convergence ball for an efficient eighth order method using only the first derivative
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Sema Journal, 2023
EXTENDED EFFICIENT HIGH CONVERGENCE ORDER SCHEMES FOR EQUATIONS
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros
Applicationes Mathematicae, 2023
We investigate the ball of convergence using only the first derivative for two sixth order algorithms for solving equations that are run under the equal set of circumstances. In addition, we provide a calculable ball comparison between the two schemes und
EXTENDED EFFICIENT HIGH CONVERGENCE ORDER SCHEMES FOR EQUATIONS
Communications in Optimization Theory, 2023
Extended three step sixth order Jarratt-like methods under generalized conditions for nonlinear equations
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda, Michael I. Argyros
Arabian Journal of Mathematics, 2022
The convergence balls as well as the dynamical characteristics of two sixth order Jarratt-like methods (JLM1 and JLM2) are compared. First, the ball analysis theorems for these algorithms are proved by applying generalized Lipschitz conditions on derivative of the first order. As a result, significant information on the radii of convergence and the regions of uniqueness for the solution are found along with calculable error distances. Also, the scope of utilization of these algorithms is extended. Then, we compare the dynamical properties, using the attraction basin approach, of these iterative schemes. At the end, standard application problems are considered to demonstrate the efficacy of our theoretical findings on ball convergence. For these problems, the convergence balls are computed and compared. From these comparisons, it is confirmed that JLM1 has the bigger convergence balls than JLM2. Also, the attraction basins for JLM1 are larger in comparison to JLM2. Thus, for numerical applications, JLM1 is better than JLM2.
Extended Comparison between Two Derivative-Free Methods of Order Six for Equations under the Same Conditions
Samundra Regmi, Ioannis K. Argyros, Christopher I. Argyros, Debasis Sharma
Fractal and Fractional, 2022
Under the same conditions, we propose the extended comparison between two derivative free schemes of order six for addressing equations. The existing convergence technique used the standard Taylor series approach, which requires derivatives up to order seven. In contrast to previous researchers, our convergence theorems only demand the first derivative. In addition, formulas for determining the region of uniqueness for the solution, convergence radii, and error estimations are suggested. As a consequence, we broaden the utility of these productive schemes. Moreover, we present a comparison of attraction basins for these schemes to obtain roots of complex polynomial equations. The confirmation of our convergence findings on application problems brings this research to a close.
A study on the local convergence and complex dynamics of Kou’s family of iterative methods
Ioannis K. Argyros, Debasis Sharma, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Sema Journal, 2022
Extended iterative schemes based on decomposition for nonlinear models
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Journal of Applied Mathematics and Computing, 2022
Extending the applicability and convergence domain of a higher-order iterative algorithm under ω condition
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Rendiconti Del Circolo Matematico Di Palermo, 2022
Extending the applicability of a fourth-order method under lipschitz continuous derivative in banach spaces
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 2022
Extended ball convergence of a seventh order derivative free method for solving system of equations with applications
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Michael I. Argyros
Journal of Analysis, 2022
On the Convergence of Harmonic Mean Newton Method Under ω Continuity Condition in Banach Spaces
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
International Journal of Applied and Computational Mathematics, 2021
Convergence of Traub's Iteration under ω Continuity Condition in Banach Spaces
D. Sharma, S. K. Parhi, S. K. Sunanda
Russian Mathematics, 2021
On the local convergence of higher order methods in banach spaces
, Debasis Sharma, Sanjaya Kumar Parhi, and
Fixed Point Theory, 2021
Extending the convergence domain of deformed Halley method under ω condition in Banach spaces
Debasis Sharma, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Boletin De La Sociedad Matematica Mexicana, 2021
Extended high order algorithms for equations under the same set of conditions
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda, Michael I. Argyros
Algorithms, 2021
On the local convergence of a third-order iterative scheme in Banach spaces
Debasis Sharma, Sanjaya Kumar Parhi
Rendiconti Del Circolo Matematico Di Palermo, 2021
Extending the app licability of modified weerakoon-fernando method with ω continuity condition in banach spaces
Indian Journal of Mathematics, 2021
A family of fifth and sixth convergence order methods for nonlinear models
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Symmetry, 2021
On the Local Convergence of Weerakoon's Method under Hölder Continuity Condition in Banach Spaces
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 2021
Local convergence of two Newton-like methods under Hölder continuity condition in Banach spaces
Debasis Sharma, Sanjaya Kumar Parhi
International Journal of Mathematics in Operational Research, 2021
GENERALIZING THE LOCAL CONVERGENCE ANALYSIS OF A CLASS OF k-STEP ITERATIVE ALGORITHMS WITH HÖLDER CONTINUOUS DERIVATIVE IN BANACH SPACES
Ioannis K. Argyros, Debasis Sharma, Sanjaya Kumar Parhi
Applicationes Mathematicae, 2021
Extending the Applicability and Convergence Domain of a Fifth-Order Iterative Scheme under Hölder Continuous Derivative in Banach Spaces
Debasis Sharma, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Contemporary Mathematics Singapore, 2021
Local convergence and dynamical analysis of a third and fourth order class of equation solvers
Debasis Sharma, Ioannis K. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Fractal and Fractional, 2021
EXTENDED BALL CONVERGENCE FOR SEVENTH ORDER DERIVATIVE FREE CLASS OF ALGORITHMS FOR NONLINEAR EQUATIONS
I.K. Argyros, D. Sharma, C.I. Argyros, S.K. Parhi, S.K. Sunanda, M.I. Argyros
Matematychni Studii, 2021
On the Convergence, Dynamics and Applications of a New Class of Nonlinear System Solvers
Ioannis K. Argyros, Debasis Sharma, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
International Journal of Applied and Computational Mathematics, 2020
On the local convergence of modified Weerakoon’s method in Banach spaces
Debasis Sharma, Sanjaya Kumar Parhi
Journal of Analysis, 2020
Complex dynamics of a sixth and seventh order family of root finding methods
Debasis Sharma, Sanjaya Kumar Parhi
Sema Journal, 2020
On the local convergence of Weerakoon–Fernando method with ω continuity condition in Banach spaces
Ioannis K. Argyros, Debasis Sharma, Sanjaya Kumar Parhi
Sema Journal, 2020
Extending the Applicability of a Newton-Simpson-Like Method
Debasis Sharma, Sanjaya Kumar Parhi
International Journal of Applied and Computational Mathematics, 2020
Local Convergence and Complex Dynamics of a Uni-parametric Family of Iterative Schemes
Debasis Sharma, Sanjaya Kumar Parhi
International Journal of Applied and Computational Mathematics, 2020
A New Class of Fifth and Sixth Order Root-Finding Methods with Its Dynamics and Applications
Debasis Sharma, Sanjaya Kumar Parhi, Shanta Kumari Sunanda
Contemporary Mathematics Singapore, 2020
An improved local analysis of deformed halley method in banach spaces
DEBASIS SHARMA, SANJAYA KUMAR PARHI, SHANTA KUMARI SUNANDA
Poincare Journal of Analysis and Applications, 2020

RECENT SCHOLAR PUBLICATIONS

Expansion of Convergence Domain of a Parameter-Based Iteration Scheme for Equations in Banach Spaces
E Martínez Molada, D Sharma
MDPI AG , 2025
2025
Expansion of Convergence Domain of a Parameter-Based Iteration Scheme for Equations in Banach Spaces
E Martínez, D Sharma
Symmetry 17 (11), 1813 , 2025
2025
Extended convergence ball for an efficient eighth order method using only the first derivative
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
SeMA Journal 80 (2), 319-331 , 2023
2023
Citations: 1
Extended ball convergence of a seventh order derivative free method for solving system of equations with applications
IK Argyros, D Sharma, CI Argyros, SK Parhi, MI Argyros
The Journal of Analysis 31 (1), 279-294 , 2023
2023
Citations: 3
Extended efficient high convergence order schemes for equations
IK Argyros, D Sharma, CI Argyros
Applicationes Mathematicae, in press. http://dx. doi. org/10.4064/am2444-2-2023 , 2023
2023
Citations: 2
Extended three step sixth order Jarratt-like methods under generalized conditions for nonlinear equations
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda, MI Argyros
Arabian Journal of Mathematics 11 (3), 443-457 , 2022
2022
Citations: 5
Ball Comparison between Two Efficient Weighted-Newton-like Solvers for Equations
IK Argyros, S Regmi, CI Argyros, D Sharma
Foundations 2 (4), 1031-1044 , 2022
2022
Extended Comparison between Two Derivative-Free Methods of Order Six for Equations under the Same Conditions
S Regmi, IK Argyros, CI Argyros, D Sharma
Fractal and Fractional 6 (11), 634 , 2022
2022
Citations: 2
A study on the local convergence and complex dynamics of Kou’s family of iterative methods
IK Argyros, D Sharma, SK Parhi, SK Sunanda
SeMA Journal 79 (2), 365-381 , 2022
2022
Extended iterative schemes based on decomposition for nonlinear models
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
Journal of Applied Mathematics and Computing 68 (3), 1485-1504 , 2022
2022
Citations: 9
Extending the local convergence of a seventh convergence order method without derivatives
IK Argyros, D Sharma, CI Argyros, SK Parhi
Foundations 2 (2), 338-347 , 2022
2022
Citations: 1
Extending the applicability and convergence domain of a higher-order iterative algorithm under condition
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
Rendiconti del Circolo Matematico di Palermo Series 2 71 (1), 469-482 , 2022
2022
Citations: 3
Extending the applicability of a fourth-order method under Lipschitz continuous derivative in Banach spaces
D Sharma, S Kumar Parhi
TWMS Journal Of Applied And Engineering Mathematics , 2022
2022
On the Convergence of Harmonic Mean Newton Method Under Continuity Condition in Banach Spaces
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
International Journal of Applied and Computational Mathematics 7 (6), 219 , 2021
2021
Citations: 1
Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda, MI Argyros
Matematychni Studii 56 (1), 72-82 , 2021
2021
Convergence of Traub's Iteration under Continuity Condition in Banach Spaces
D Sharma, SK Parhi, SK Sunanda
Russian Mathematics 65 (9), 52-68 , 2021
2021
Citations: 3
Extended High Order Algorithms for Equations under the Same Set of Conditions
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda, MI Argyros
Algorithms 14 (7), 207 , 2021
2021
On the local convergence of higher order methods in Banach spaces
D Sharma, SK Parhi
Fixed Point Theory 22 (2), 855-870 , 2021
2021
Citations: 11
Extending the convergence domain of deformed Halley method under condition in Banach spaces
D Sharma, SK Parhi, SK Sunanda
Boletin de la Sociedad Matematica Mexicana 27 (2), 32 , 2021
2021
Citations: 6
On the Local Convergence
SK Parhi, D Sharma
New Trends in Applied Analysis and Computational Mathematics: Proceedings of … , 2021
2021

MOST CITED SCHOLAR PUBLICATIONS

On the local convergence of Weerakoon–Fernando method with continuity condition in Banach spaces
IK Argyros, D Sharma, SK Parhi
SeMA Journal 77 (3), 291-304 , 2020
2020.0
Citations: 19
On the local convergence of modified Weerakoon’s method in Banach spaces
D Sharma, SK Parhi
The Journal of Analysis 28 (3), 867-877 , 2020
2020.0
Citations: 16
On the local convergence of higher order methods in Banach spaces
D Sharma, SK Parhi
Fixed Point Theory 22 (2), 855-870 , 2021
2021.0
Citations: 11
A family of fifth and sixth convergence order methods for nonlinear models
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
Symmetry 13 (4), 715 , 2021
2021.0
Citations: 10
Extending the applicability of a Newton-Simpson-like method
D Sharma, SK Parhi
International Journal of Applied and Computational Mathematics 6 (3), 79 , 2020
2020.0
Citations: 10
Extended iterative schemes based on decomposition for nonlinear models
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
Journal of Applied Mathematics and Computing 68 (3), 1485-1504 , 2022
2022.0
Citations: 9
Local convergence and complex dynamics of a uni-parametric family of iterative schemes
D Sharma, SK Parhi
International Journal of Applied and Computational Mathematics 6 (3), 83 , 2020
2020.0
Citations: 8
On the local convergence of a third-order iterative scheme in Banach spaces
D Sharma, SK Parhi
Rendiconti del Circolo Matematico di Palermo Series 2, 1-15 , 2020
2020.0
Citations: 8
On the convergence, dynamics and applications of a new class of nonlinear system solvers
IK Argyros, D Sharma, SK Parhi, SK Sunanda
International Journal of Applied and Computational Mathematics 6 (5), 142 , 2020
2020.0
Citations: 7
Extending the convergence domain of deformed Halley method under condition in Banach spaces
D Sharma, SK Parhi, SK Sunanda
Boletin de la Sociedad Matematica Mexicana 27 (2), 32 , 2021
2021.0
Citations: 6
Extended three step sixth order Jarratt-like methods under generalized conditions for nonlinear equations
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda, MI Argyros
Arabian Journal of Mathematics 11 (3), 443-457 , 2022
2022.0
Citations: 5
Local convergence and dynamical analysis of a third and fourth order class of equation solvers
D Sharma, IK Argyros, SK Parhi, SK Sunanda
Fractal and Fractional 5 (2), 27 , 2021
2021.0
Citations: 5
On the local convergence of Weerakoon-Fernando method with ω continuity condition in Banach spaces. SeMA J.(2020)
IK Argyros, D Sharma, SK Parhi
DOI: https://doi. org/10.1007/s40324-020-00217-y , 0
Citations: 4
Extended ball convergence of a seventh order derivative free method for solving system of equations with applications
IK Argyros, D Sharma, CI Argyros, SK Parhi, MI Argyros
The Journal of Analysis 31 (1), 279-294 , 2023
2023.0
Citations: 3
Extending the applicability and convergence domain of a higher-order iterative algorithm under condition
IK Argyros, D Sharma, CI Argyros, SK Parhi, SK Sunanda
Rendiconti del Circolo Matematico di Palermo Series 2 71 (1), 469-482 , 2022
2022.0
Citations: 3
Convergence of Traub's Iteration under Continuity Condition in Banach Spaces
D Sharma, SK Parhi, SK Sunanda
Russian Mathematics 65 (9), 52-68 , 2021
2021.0
Citations: 3
Local convergence of two Newton-like methods under Hölder continuity condition in Banach spaces
D Sharma, SK Parhi
International Journal of Mathematics in Operational Research 19 (4), 500-514 , 2021
2021.0
Citations: 3
Complex dynamics of a sixth and seventh order family of root finding methods
D Sharma, SK Parhi
SeMA Journal, 1-11 , 2020
2020.0
Citations: 3
Extended efficient high convergence order schemes for equations
IK Argyros, D Sharma, CI Argyros
Applicationes Mathematicae, in press. http://dx. doi. org/10.4064/am2444-2-2023 , 2023
2023.0
Citations: 2
Extended Comparison between Two Derivative-Free Methods of Order Six for Equations under the Same Conditions
S Regmi, IK Argyros, CI Argyros, D Sharma
Fractal and Fractional 6 (11), 634 , 2022
2022.0
Citations: 2