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3,046 results on '"Kumam, Poom"'

205. A viscosity-type scheme for optimization problems in Hadamard spaces with applications.

Author

Salisu, Sani, Kumam, Poom, and Sriwongsa, Songpon

Subjects
*SET-valued maps, *VECTOR fields, *PROBLEM solving, *PROBABILITY theory, *ROBOTICS, *NONEXPANSIVE mappings
Abstract

In this article, we propose a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multi-valued nonexpansive mapping in the framework of Hadamard spaces. We obtain a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fréchet mean, find the mean of probabilities, minimize energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature. [ABSTRACT FROM AUTHOR]

Published
2024
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206. Golden ratio method for solving monotone variational inequality problems in Hadamard spaces.

Author

Salisu, Sani, Sriwongsa, Songpon, and Kumam, Poom

Subjects
GOLDEN ratio, VARIATIONAL inequalities (Mathematics), MONOTONE operators, GEODESICS
Abstract

In this article, a generalized variational inequality problem in the setting of Hadamard spaces is introduced and analyzed. For approximating a solution of the problem when the underlined mapping is monotone, an adaptive algorithm that requires the computation of only one proximal operator at each iteration is proposed. The work gives a step towards investigating monotone variational inequality problems in geodesic settings. [ABSTRACT FROM AUTHOR]

Published
2024
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207. A contribution to best proximity point theory and an application to partial differential equation.

Author

Termkaew, Sakan, Chaipunya, Parin, Gopal, Dhananjay, and Kumam, Poom

Subjects
PARTIAL differential equations, METRIC spaces, SET-valued maps, CAUCHY sequences, NONEXPANSIVE mappings
Abstract

In this work, the main discussion centres on avoiding the use of triangle inequality while proving Cauchy sequence to establish best proximity point theorems for single valued as well as multivalued non-self mappings. We prove such best proximity point theorems in the setting of non-triangular metric spaces and elaborate through examples. In this process host of the existing best proximity results are generalized and improved. To arouse further interest in the subject, we connect this work in solving a specific type of partial differential equation problem. [ABSTRACT FROM AUTHOR]

Published
2024
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213. Approximate analytical fractional view of convection–diffusion equations

Author

Khan Hassan, Mustafa Saima, Ali Izaz, Kumam Poom, Baleanu Dumitru, and Arif Muhammad

Subjects
variational iteration method, homotopy perturbation method, convection–diffusion equations, laplace transform method, mittag–leffler function, Physics, QC1-999
Abstract

In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection–diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.

Published
2020
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