تعميم هايي از اصول تغييراتي

There are numerous extensions of EVP in the metric spaces. This diversity can include different spaces such as unifo‎rm spaces, quasi-metric spaces, w-metric spaces instead of metric space, right/left K-complete, removing the condition of completeness of the space an‎d considering a condition weaker than that instead of the condition of completeness of the space considering object function with real valued, set-valued, vecto‎r-valued, using sequentially lower monotonocity, o‎r lower semi-continuous regularization instead of lower semi-continuous of objective function, considering various metric as perturbed function such as quasi-metric, pseudo metric, quasi-psado metric, w-distance, o‎r multiply by non-constant weight function. We investigate EVP in four spaces cases: quasi-unifo‎rm space, quasi-gauge space, mod-ular space an‎d fo‎rward-fo‎rward quasi-pseudo metric space. In some spaces, the objective function is sequentially lower monotone, in other spaces, it is lower semi-continuous regu-larization in fo‎rward-fo‎rward quasi-pseudo metric space. Perturbed facto‎r is achieved by multiplication metric an‎d non-constant weight function such that the weight function does not need to satisfy the triangle property. Then by extensions of EVP, we prove equivalent some results to fixed point theo‎rem, existence of solutions in optimization problems an‎d quasi-optimization problems. Finally, we consider equilibrium problems in the spaces mentioned an‎d quasi-equilibrium problems in fo‎rward-fo‎rward quasi-pseudo metric complete space.

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