Purvee Bhardwaj
Purvee Bhardwaj has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Ramakant Bhardwaj
Amity University Kolkata WB
3 shared publications - Satyendra Narayan
Algoma University
3 shared publications - Kushal Guha Bakshi
Applied Science Department, Amity University Kolkata, Kolkata 700135, India
2 shared publications - Sagnik Sinha
Department of Mathematics, Jadavpur University, Kolkata 700075, India
2 shared publications - Deb Sarkar
Department of Mathematics, Amity University Kolkata, Kadampukur 700135, West Bengal, India
1 shared publication - Sonam
Department of Mathematics, Amity University Kolkata, Kadampukur 700135, West Bengal, India
1 shared publication
Latest Publications
- Open Access
- 30 June 2026
- Published by MDPI AG in Algorithms
- Vol. 19 (7) , 529
Undiscounted Semi-Markov Decision Processes with Countably Infinite Action Spaces
In this article, we study semi-Markov decision processes (SMDPs) under the limiting ratio average (undiscounted) pay-off criterion, where the state space is finite and the action space of the decision maker is possibly countably infinite. We impose no restriction on the reward function. We prove that the value of such an SMDP exists and that the decision maker possesses a near-optimal (-optimal) deterministic (pure) semi-stationary strategy, and we give a truncation-based algorithm that computes the value and such a strategy in finite time by solving a finite linear program at each truncation level. We analyze the algorithm’s computational complexity, showing that each truncation level is solved in time polynomial in the number of state–action pairs, while the number of levels required for termination depends on the prescribed accuracy and on the model. We further establish a certified, computable bound on the truncation error under bounded rewards together with standard ergodicity and tail-regularity conditions, yielding a stopping rule that guarantees a prescribed accuracy; we delimit precisely the regime in which such a certificate exists. Numerical experiments, including randomly generated instances, illustrate the algorithm and its computational behavior. Finally, under standard ergodicity conditions, we derive an optimality equation for these SMDP models.- 30 June 2026
- Published by MDPI AG in Algorithms
- Vol. 19 (7) , 529
Open AccessUndiscounted Semi-Markov Decision Processes with Countably Infinite Action Spaces
In this article, we study semi-Markov decision processes (SMDPs) under the limiting ratio average (undiscounted) pay-off criterion, where the state space is finite and the action space of the decision maker is possibly countably infinite. We impose no restriction on the reward function. We prove that the value of such an SMDP exists and that the decision maker possesses a near-optimal (-optimal) deterministic (pure) semi-stationary strategy, and we give a truncation-based algorithm that computes the value and such a strategy in finite time by solving a finite linear program at each truncation level. We analyze the algorithm’s computational complexity, showing that each truncation level is solved in time polynomial in the number of state–action pairs, while the number of levels required for termination depends on the prescribed accuracy and on the model. We further establish a certified, computable bound on the truncation error under bounded rewards together with standard ergodicity and tail-regularity conditions, yielding a stopping rule that guarantees a prescribed accuracy; we delimit precisely the regime in which such a certificate exists. Numerical experiments, including randomly generated instances, illustrate the algorithm and its computational behavior. Finally, under standard ergodicity conditions, we derive an optimality equation for these SMDP models. - Open Access
- 15 May 2026
- Published by MDPI AG in Preprints.org
Undiscounted Semi-Markov Decision Processes With Countably Infinite Action Spaces
In this article we study semi-Markov decision processes (SMDPs) where the pay-off criterion is limiting ratio average, generally known as undiscounted pay-off. Here we consider the action space of the decision maker to be possibly countably infinite. However, we do not put any restriction on the reward function. We prove the existence of a near-optimal or ϵ-optimal strategy of the decision maker which turns out to be a deterministic semi-stationary. An efficient algorithm is discussed to compute a near-optimal pure semi-stationary strategy for such SMDP model. Also under some standard ergodicity conditions, we propose an optimality equation of these SMDP models.
- 15 May 2026
- Published by MDPI AG in Preprints.org
Open AccessUndiscounted Semi-Markov Decision Processes With Countably Infinite Action Spaces
In this article we study semi-Markov decision processes (SMDPs) where the pay-off criterion is limiting ratio average, generally known as undiscounted pay-off. Here we consider the action space of the decision maker to be possibly countably infinite. However, we do not put any restriction on the reward function. We prove the existence of a near-optimal or ϵ-optimal strategy of the decision maker which turns out to be a deterministic semi-stationary. An efficient algorithm is discussed to compute a near-optimal pure semi-stationary strategy for such SMDP model. Also under some standard ergodicity conditions, we propose an optimality equation of these SMDP models.
- Open Access
- 22 August 2025
- Published by MDPI AG in AppliedMath
- Vol. 5 (3) , 108
Solutions of Nonlinear Differential and Integral Equations via Optimality Results Involving Proximal Mappings
This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in extending fixed-point theory. Through introducing this innovative concept, the study provides a theoretical framework for analyzing mappings in diverse scenarios. In this study, we introduce the concept of best proximity point (BPP) within the framework of orthogonal fuzzy metric spaces by employing orthogonal fuzzy proximal contractive mappings. Moreover, this research explores the implications of the established results, considering both self-mappings and non-self mappings that share the same parameter set. Additionally, some examples are provided to illustrate the practical relevance of the proven results and consequences in various mathematical contexts. The findings of this study can open up avenues for further exploration and application in solving real-world problems.
- 22 August 2025
- Published by MDPI AG in AppliedMath
- Vol. 5 (3) , 108
Open AccessSolutions of Nonlinear Differential and Integral Equations via Optimality Results Involving Proximal Mappings
This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in extending fixed-point theory. Through introducing this innovative concept, the study provides a theoretical framework for analyzing mappings in diverse scenarios. In this study, we introduce the concept of best proximity point (BPP) within the framework of orthogonal fuzzy metric spaces by employing orthogonal fuzzy proximal contractive mappings. Moreover, this research explores the implications of the established results, considering both self-mappings and non-self mappings that share the same parameter set. Additionally, some examples are provided to illustrate the practical relevance of the proven results and consequences in various mathematical contexts. The findings of this study can open up avenues for further exploration and application in solving real-world problems.