On the C ∗ -algebra valued G-metric space related with fixed point theorems

Abstract

There are many fixed point results in the various kinds of metric spaces such as b-metric spaces, quaternion metric spaces, G-metric spaces, uniform spaces, non-commutative Banach spaces etc. In this work, we consider the one of modern methods as C * -algebra G-metric space with fixed point theory to solve problems above mentioned. We prove the fixed point theorems for a mapping under the contractive conditions in C * -algebra G-metric space. Besides, we establish the not only existence but also uniqueness theorem of fixed point in the such space. Also, we provide several examples to put support behind our main result.

Problem Involving the Riemann–Liouville Derivative and Implicit Variable-Order Nonlinear Fractional Differential Equations

“…Recently, several researchers contributed in this feld with many published papers that are concerned with the study to many diferent problems of fractional diferential equations, e.g., Borisut et al [6] presented the ψ-Hilfer fractional differential equation with nonlocal multipoint condition, Ahmad et al [7] investigated a fractional-order compartmental HIV and malaria coinfection epidemic model using the Caputo derivative, and Özer et al [8][9][10][11][12] established the existence and uniqueness of the common fxed point theorem in c * -algebra valued b-metric spaces, see [6,[13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”