Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces

Abstract

In this paper, we prove fixed point theorem via orthogonal Geraghty type α-admissible contraction map in an orthogonal complete Branciari b-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically.

Existence of common fuzzy fixed points via fuzzy F-contractions in b-metric spaces

“…Recently, Kanwal et al 17 obtained common fixed points of L -fuzzy mappings satisfying -contractions in complete b -metric spaces. Dhanraj et al 27 , Gopal et al 28 , 29 , Lakzian et al 30 , Mani et al 31 , 32 and Nallaselli et al 33 have established many wonderful results in b-metric spaces and its generalizations for F- contractions and some other contractive conditions. Moreover, they have offered the applications of the obtained results, see references therein for details.…”

New Fixed Point Theorems on Complete b-Metric Space by Using Rus Contraction Mapping

“…Many researchers developed fixed point theory and applied it in the field of core mathematics. Recently, Dhanraj et al [8] studied "Solution to integral equation in an O-complete Branciari b-metric spaces", Senthil Kumar et al [16] studied "Fixed point for an OgF-c in O-complete b-metric-like spaces", Gnanaprakasam et al [9] studied "New fixed point results in orthogonal b--metric spaces with related applications", Mani et al [13] studied "Fixed point results in C*-algebra-valued partial b-metric spaces with related application", Mani et al [14] studied "Solution of Fredholm integral equation via common fixed point theorem on bicomplex valued b-metric space", Gholidahneh et al [10] studied "The Meir-Keeler type contractions in extended modular b-metric spaces with an application", etc.…”