Abstract
In the present work, we propose a dierent reciprocal second power Functional Equation (FE) which involves the arguments of functions in rational form and determine its stabilities in the setting of modular spaces with and without using Fatou property. We also prove the stabilities in beta-homogenous spaces. As an application, we associate this equation with the electrostatic forces of attraction between unit charges in various cases using Coloumb's law.
Highlights
Introduction & PreliminariesThe hypothesis connected with linear spaces and the concepts of modular spaces were dealt in [20]
We propose a different reciprocal second power Functional Equation (FE) of the form uv uv mq 2u + v + mq 2u − v = 2mq(u) + 8mq(v)
We explore the investigate stability results of equation (1) connected with modular theory with modular space Uμ without applying the Fatou property
Summary
Introduction & PreliminariesThe hypothesis connected with linear spaces and the concepts of modular spaces were dealt in [20]. Without the application of ∆2-condition, proposed in [7], there are many stability problems via fixed point theorem of quasicontracion functions in the setting of modular spaces.
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