Quadruple random common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

Abstract

In this paper, we introduce the concept of cone b-metric spaces over Banach algebras and present some quadruple random coincidence points and quadruple random common fixed point theorems for nonlinear operators in such spaces. Keywords:Quadruple random fixed point, quadruple common random fixed point, quadruple random coincidence point, cone b-metric space over Banach algebra.

Fixed point results for weak contractions in partially ordered b-metric space

“…A b -metric space is one of several generalizations of a standard metric space proposed by Bakhtin in his work [ 9 ], and widely used by Czerwik in his work [ 14 , 15 ]. Following that, a lot of progress was made in acquiring the results of fixed points to single valued as well as multi-valued operators in the space, as evidenced by [ 1 , 2 , 4 – 8 , 10 , 13 , 16 – 18 , 20 , 21 , 23 , 24 , 26 , 27 , 31 , 38 – 41 ].…”

Generalized Ekeland’s variational principle with applications

“…On the other hand, since T is complete, {v n } converges toq ∈ T. Let S = sup n∈N w n Γ (p, p,p). Then, from (5.4) and (Γ 2 ), we have As a new approach, one can generalize the results presented in [12][13][14][15][16][17][18][19][20][21] in q-F-m spaces with Γ -distance.…”