Strong convergence of an inertial iterative method for generalized nonexpansive mappings in Banach spaces Prashant Patel, Rahul Shukla Applied General Topology, 2026 We introduce an iterative technique with an inertial term that converges strongly to a fixed point of mappings satisfying Condition (E). Our results extend existing work by providing a robust numerical method for solving fixed point problems in Banach spaces. To demonstrate the effectiveness of our approach, we present numerical examples of a mapping that is not nonexpansive but satisfies Condition (E). Furthermore, we illustrate the convergence behaviour of our algorithm for different choices of initial guesses and coefficients, using MATLAB to validate the theoretical results. This work contributes to the broader framework of fixed point theory and offers practical insights for solving nonlinear problems in applied mathematics.
A New Fixed-Point Framework for Nonexpansive and Averaged Mappings in Normed GE-Algebras Prashant Patel, Ravikumar Bandaru, Amal S. Alali Journal of Mathematics, 2026 In this paper, we develop a systematic framework for studying fixed‐point theory in the setting of normed GE‐algebras. Building on the GE‐norm, we introduce and analyze nonexpansive mappings, α ‐averaged mappings, and enriched contractions with respect to the quasimetric induced by the GE‐norm. Several new fixed point results are established, including the nonexpansiveness of averaged operators, a demiclosedness principle, and the sequential closedness of fixed‐point sets. We further prove convergence theorems for Picard‐type iterations associated with α ‐averaged and enriched nonexpansive mappings, thereby extending classical fixed point principles from normed linear and metric spaces to the broader, nonsymmetric, and algebraic setting of GE‐algebras. The results presented here demonstrate that normed GE‐algebras provide a natural and robust framework for nonlinear operator theory and open new directions for fixed point analysis within algebraic systems.
Prioritizing Sustainability Dimensions in Locally Focused Tourism: An Advanced Ranking Approach Saurabh Srivastav, Prashant Patel, Rahul Shukla Discrete Dynamics in Nature and Society, 2026 Locally focused tourism (LFT) promotes sustainable development by prioritizing local community empowerment through local engagement, preservation of cultural traditions, and equitable economic participation. However, aligning these local development goals with the interests of tourism investors and authorities is still a significant challenge. The current study addresses this gap by ranking four key sustainability pillars, namely, economic, environmental, social, and cultural sustainability with a hybrid soft computing approach combining fuzzy sets and the analytic hierarchy process (AHP), that is, fuzzy AHP. Findings reveal environmental sustainability as the highest priority, followed by economic, cultural, and social dimensions. An intelligent information system was developed to find these rankings, serving as a decision‐support tool for both policymakers and tourism administrators. The framework balances both the investment priorities and LFT values, by offering a path toward long‐term, environmentally responsible, and culturally sensitive tourism planning, and is achieved by systematically prioritizing sustainability dimensions through expert‐driven soft computing modeling, which ensures environmental and community‐centric factors are not dominated by purely economic interests, while still acknowledging investment viability.
Hierarchical Fixed Point Results for a Countable Family of Strict Pseudo-Contractive Mappings in Hadamard Manifolds Prashant Patel, Rahul Shukla European Journal of Pure and Applied Mathematics, 2025 The aim of this paper is to present convergence results for a countable family of strict pseudocontractive mappings in Hadamard manifolds. More precisely, we employ the shrinking projection method to approximate common hierarchical fixed points of a countable family of strict pseudocontractive mappings in the setting of Hadamard manifolds. We also present some nontrivial examples to illustrate our result.
VISCOSITY APPROXIMATION METHODS FOR SPLIT MONOTONE VARIATIONAL INCLUSIONS AND FIXED POINT PROBLEMS OF A FINITE FAMILY OF ξ-DEMIMETRIC MAPPINGS Australian Journal of Mathematical Analysis and Applications, 2025
Optimization of Parameters of the OWC Wave Energy Converter Device Using a Machine Learning Approach Kush Karnavat, Nilansh Vadodaria, Kshma Trivedi, Prashant Patel 2025 5th International Conference on Advances in Electrical Computing Communication and Sustainable Technologies Icaect 2025, 2025 In this study, the performance of an L-shaped front wall OWC (Oscillating Water Column) device is investigated in the presence of irregular incident waves. To efficiently explore the complex interactions between input features and the target variable, two supervised machine learning models: (i) a decision tree model and (ii) an XGBoost model are considered. The input parameters selected for this analysis are: OWC Front wall Draft, OWC Duct Length, Chamber Length, ripple Number, and ripple amplitude of the sinusoidal seabed. The output attribute is the maximum power extracted by the OWC device. The XG Boost model is used to identify critical input regions where power extraction peaks, while the decision tree model further aids in understanding the parameter influences on power extraction. A dataset of 3125 samples was generated for training, validation, and testing. By employing accumulated local effect plots with the XG Boost model, five specific regions in the input space were identified that maximize annual average power extraction. The results indicate that optimal power extraction is achieved for a specific value of each parameter, thereby validating the influence of each on OWC device performance.
Normal Paradistributive Latticoids Ravikumar Bandaru, Prashant Patel, Noorbhasha Rafi, Rahul Shukla, Suryavardhani Ajjarapu European Journal of Pure and Applied Mathematics, 2024
Common Solution for Fixed Points of a Finite Family of Nonexpansive Mappings and Variational Inclusion Problem Palestine Journal of Mathematics, 2024
SOLVING FIXED POINT PROBLEMS AND VARIATIONAL INCLUSIONS USING VISCOSITY APPROXIMATIONS Australian Journal of Mathematical Analysis and Applications, 2024
A New Fixed‐Point Framework for Nonexpansive and Averaged Mappings in Normed GE‐Algebras P Patel, R Bandaru, AS Alali Journal of Mathematics 2026 (1), 7377821 , 2026 2026
Strong convergence of an inertial iterative method for generalized nonexpansive mappings in Banach spaces P Patel, R Shukla Applied general topology 27 (1), 24241-24241 , 2026 2026
Prioritizing Sustainability Dimensions in Locally Focused Tourism: An Advanced Ranking Approach S Srivastav, P Patel, R Shukla Discrete Dynamics in Nature and Society 2026 (1), 1452547 , 2026 2026
Hemicomplemented Almost Distributive Lattices N Rafi, P Patel, RK Davala, R Shukla European Journal of Pure and Applied Mathematics 18 (4), 6249-6249 , 2025 2025 Citations: 1
Strong Convergence Algorithms for Split Common Fixed Point Problems Involving Demicontractive Mappings P Patel, R Shukla Adv. Fixed Point Theory 15 (2025) , 2025 2025
Iterative Techniques for Common Solutions of Mixed Equilibrium Problem and Fixed Points of µ-Demicontractive Mappings P Patel, R Shukla Asia Pacific Journal of Mathematics 12 (2025) , 2025 2025
Viscosity Approximation Methods for Split Monotone Variational Inclusion and Fixed Point Problems of a Finite Family of ξ-Demimetric Mappings P Patel, R Shukla Australian Journal of Mathematical Analysis and Applications 22 (2), 11 , 2025 2025
Hierarchical Fixed Point Results for a Countable Family of Strict Pseudo-Contractive Mappings in Hadamard Manifolds P Patel, R Shukla European Journal of Pure and Applied Mathematics 18 (2), 5951-5951 , 2025 2025
A Unified Characterization of Congruence Co-Kernels in Paradistributive Latticoids R Bandaru, P Patel, RP Panda, R Shukla International Journal of Mathematics and Computer Science 20 (2), 671–678 , 2025 2025
Common Solution for a Finite Family of Equilibrium Problems, Finite Family of Inclusion Problems and Fixed Points of a Nonexpansive Mapping in Hadamard Manifolds P Patel, R Shukla Boletim da Sociedade Paranaense de Matemática 43 (2025), 1-12 , 2025 2025
Optimization of Parameters of the OWC Wave Energy Converter Device Using a Machine Learning Approach K Karnavat, N Vadodaria, K Trivedi, P Patel Fifth International Conference on Advances in Electrical, Computing … , 2025 2025
Common Solution for Fixed Points of a Finite Family of Nonexpansive Mappings and Variational Inclusion Problem P Patel Palestine Journal of Mathematics 13 (4), 337–345 , 2025 2025
Viscosity Approximation for Split Equality Generalized Mixed Equilibrium Problems With Semigroups of Nonexpansive Mappings P Patel, R Shukla Abstract and Applied Analysis 2024 (1), 13 , 2024 2024 Citations: 1
Solving Fixed Point Problems and Variational Inclusions Using Viscosity Approximations P Patel, R Shukla Australian Journal of Mathematical Analysis and Applications 21 (2), 13 , 2024 2024 Citations: 1
Viscosity Approximation Methods for Generalized Modification of the System of Equilibrium Problem and Fixed Point Problems of an Infinite Family of Nonexpansive Mappings P Patel, R Shukla Mathematics and Statistics 12 (4), 339-347 , 2024 2024 Citations: 3
Approximating zeros of monotone operators in Banach spaces R Pant, P Patel Advances in Fixed Point Theory 14 , 2024 2024
Consistent Ideals of Pseudo-Complemented Lattices N Rafi, RK Bandaru, P Patel, R Shukla Asia Pacific Journal of Mathematics 11 , 2024 2024
Normal paradistributive latticoids R Bandaru, P Patel, N Rafi, R Shukla, S Ajjarapu European Journal of Pure and Applied Mathematics 17 (2), 1306-1320 , 2024 2024 Citations: 4
Common Solution for a Finite Family of Equilibrium Problems, Inclusion Problems and Fixed Points of a Finite Family of Nonexpansive Mappings in Hadamard Manifolds P Patel, R Shukla Sahand Communications in Mathematical Analysis 21 (1), 255-271 , 2024 2024 Citations: 6
Mann-Dotson's algorithm for a countable family of non-self strict pseudo-contractive mappings P Patel, R Shukla Rendiconti del Circolo Matematico di Palermo Series 2 , 2023 2023 Citations: 8
MOST CITED SCHOLAR PUBLICATIONS
Nonexpansive Mappings and Their Extensions and Generalizations in Banach Spaces R Pant, R Shukla, P Patel Metric Fixed Point Theory: Applications in Science, Engineering and … , 2021 2021 Citations: 26
Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces R Pant, P Patel, R Shukla, MDL Sen Symmetry 13 (4), 585 , 2021 2021 Citations: 17
Mann-Dotson's algorithm for a countable family of non-self strict pseudo-contractive mappings P Patel, R Shukla Rendiconti del Circolo Matematico di Palermo Series 2 , 2023 2023 Citations: 8
Fixed point results for a class of nonexpansive type mappings in Banach spaces R Pant, P Patel, R Shukla Advances in the Theory of Nonlinear Analysis and its Application 5 (3), 368-381 , 2021 2021 Citations: 8
Common Solution for a Finite Family of Equilibrium Problems, Inclusion Problems and Fixed Points of a Finite Family of Nonexpansive Mappings in Hadamard Manifolds P Patel, R Shukla Sahand Communications in Mathematical Analysis 21 (1), 255-271 , 2024 2024 Citations: 6
Viscosity Approximation Methods for Quasi-Nonexpansive Mappings in Banach Spaces P Patel, R pant FILOMAT 35 (9), 3113-3126 , 2021 2021 Citations: 6
Mann-Dotson's algorithm for a countable family of non-self Lipschitz mappings in hyperbolic metric space P Patel, R Shukla Topological Algebra and its Applications 11 (1), 20220134 , 2023 2023 Citations: 5
Normal paradistributive latticoids R Bandaru, P Patel, N Rafi, R Shukla, S Ajjarapu European Journal of Pure and Applied Mathematics 17 (2), 1306-1320 , 2024 2024 Citations: 4
The numerical solution of Boussinesq equation for shallow water waves P Patel, P Kumar, Rajni AIP Conference Proceedings 2214 (1), 020019 , 2020 2020 Citations: 4
Viscosity Approximation Methods for Generalized Modification of the System of Equilibrium Problem and Fixed Point Problems of an Infinite Family of Nonexpansive Mappings P Patel, R Shukla Mathematics and Statistics 12 (4), 339-347 , 2024 2024 Citations: 3
Hemicomplemented Almost Distributive Lattices N Rafi, P Patel, RK Davala, R Shukla European Journal of Pure and Applied Mathematics 18 (4), 6249-6249 , 2025 2025 Citations: 1
Viscosity Approximation for Split Equality Generalized Mixed Equilibrium Problems With Semigroups of Nonexpansive Mappings P Patel, R Shukla Abstract and Applied Analysis 2024 (1), 13 , 2024 2024 Citations: 1
Solving Fixed Point Problems and Variational Inclusions Using Viscosity Approximations P Patel, R Shukla Australian Journal of Mathematical Analysis and Applications 21 (2), 13 , 2024 2024 Citations: 1
Wave spectrum analysis for extreme wave oscillation inside Paradip port Gulshan, P Kumar, P Patel, Rupali, S Kaur AIP Conference Proceedings 2061 (1), 020010 , 2019 2019 Citations: 1
A New Fixed‐Point Framework for Nonexpansive and Averaged Mappings in Normed GE‐Algebras P Patel, R Bandaru, AS Alali Journal of Mathematics 2026 (1), 7377821 , 2026 2026
Strong convergence of an inertial iterative method for generalized nonexpansive mappings in Banach spaces P Patel, R Shukla Applied general topology 27 (1), 24241-24241 , 2026 2026
Prioritizing Sustainability Dimensions in Locally Focused Tourism: An Advanced Ranking Approach S Srivastav, P Patel, R Shukla Discrete Dynamics in Nature and Society 2026 (1), 1452547 , 2026 2026
Strong Convergence Algorithms for Split Common Fixed Point Problems Involving Demicontractive Mappings P Patel, R Shukla Adv. Fixed Point Theory 15 (2025) , 2025 2025
Iterative Techniques for Common Solutions of Mixed Equilibrium Problem and Fixed Points of µ-Demicontractive Mappings P Patel, R Shukla Asia Pacific Journal of Mathematics 12 (2025) , 2025 2025
Viscosity Approximation Methods for Split Monotone Variational Inclusion and Fixed Point Problems of a Finite Family of ξ-Demimetric Mappings P Patel, R Shukla Australian Journal of Mathematical Analysis and Applications 22 (2), 11 , 2025 2025
