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The problem studied is formulated in the title: proper mass variation undergravitational and Coulomb force action in Relativistic Mechanics of pointparticle. The novelty is that equations of motion are obtained in therelativistic Lagrangean framework for conservative force fields underassumption of field dependent proper mass. The dependence of proper mass onfield strength is derived from the equations of particle motion. The result isthe elimination of a classical 1/r divergence. It is shown that a photon in agravitational field may be described in terms of a refracting massless medium.This makes the gravity phenomenon compatible with SR Dynamic framework. Newresults concerning gravitational properties of particle and photon, as well asan experimental test of predicted deviation from 1/r^2 classical Coulomb forcelaw are discussed. The conclusion is made that the approach of field-dependentproper mass is perspective for better understanding GR problems and furtherstudies on divergence-free field theory development.  Key words: Relativity; gravity; Coulomb; particle; photon; speed of light;proper mass variation.  PACS: 03.30.+p, 04.20.-g

Proper Mass Variation under Gravitational and Coulomb Force Action in Relativistic Mechanics of Point Particle