APPLICATION OF FOURTH POWER TYPE CONTRACTION IN G-METRIC SPACES

Abstract

Fixed point theory is an important discipline in mathematics because of its results which are utilized to investigate the existence of solutions for the problems in applied sciences and engineering. Many fixed point results have been widely generalized throughoutthe years in various directions by introducing new metric spaces and setting of new contrac-tion mappings. The results in fixed point theory can be noticed in geometry, computational algorithms, economics, uid dynamics, micro-structures, nonlinear sciences, medical fields and optimization theory. Recently, Feng Gu and Hongqing Ye introduced third power type contraction mappings and also established related fixed point theorems under G-metric. Inthis article, we introduce new fourth power type contraction conditions in G-metric space.Further, the obtained fixed point of a fourth power contraction is proved as a G-contractive fixed point. In addition, eigen value problem will be solved as an application of fourth power contraction.