Orthogonal F-Contraction Mapping on O-Complete Metric Space with Applications

Abstract

In this paper, we introduce orthogonal concepts concerning F -contraction mappings and demonstrate some fixed-point theorems for self-mapping in a complete orthogonal metric space. Some well-known results in the literature are generalized and modified based on the demonstrated results. An example is provided to support our results, which are used in an application.

Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

“…Remark 1. If we take α(e, κ) = 1 for all e, κ ∈ P in Corollary 10 then we can derive the main result of Mani et al [7].…”

“…Gordji et al [6] took things a step further by incorporating orthogonality into MSs, leading to the concept of orthogonal metric spaces (O-MSs) and associated some results for contraction mappings. Later, Mani et al [7] and Gungor et al [8] utilized the concept of O-MSs and investigated fixed points for various generalized contractions. In 2018, Jleli et al [9] began the motion of F-metric space (F-MS) as a broadened framework encompassing both MSs and b-MSs.…”

Fixed Point Results for α , ⊥ F

“…If we take αðℏ, ςÞ = 1, for all ℏ, ς ∈ R in Theorem 16, then we get the following result of Mani et al [31].…”

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

“…And also, Eshaghi Gordji and Habibi [22] has extended and proved some fixed point theorem in generalized O-metric spaces. For other results related to orthogonal concepts, see [23][24][25][26][27][28][29][30].…”