On the Iterative Multivalued ⊥-Preserving Mappings and an Application to Fractional Differential Equation

Abstract

In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation’s solution.

Application to fixed point theory of α-θ-E-Geraghty Pata proximal contractions

“…Since {℘ i } is Cauchy and equation ( 19) satisfies for all ε ∈ [0, 1]. Limiting we have lim i→+∞ E(℘ i −1 , ℘ i ) = 0 and for particular ε = 0, equation (19) gives Corollary 2. In a complete regular partially ordered metric space (℧, ζ, ⪯), let U, V are closed nonempty subsets and ξ be an…”

“…Utilizing both Hausdorff and δ-distances, we define and demonstrate some conclusions about contractions for multivalued mappings (see [18,19] for more outcomes in this area) that are satisfying contraction conditions similar to our contractions. In a metric space (℧, ζ), let…”

Fixed Point Results via Orthogonal (α − 𝔶 − 𝔾)-Contraction in Orthogonal Complete Metric Space

“…But since δ ∈ I is arbitrary, it shows that x ≥ 1 and hence x ∈ U. Therefore, the differential equation (20) makes it easy to find x * ∈ C(I), i.e., a fixed point of M. Let x, y ∈ C(I) such that ξ(x(δ), y(δ)) ≥ 0 for all δ ∈ I. Therefore, all the conditions of the Theorem 6 are satisfied.…”

“…In 2017, Hussain et al [10] improved and expanded certain fixed point theorems for generalized G-contractive axioms in complete metric space occupation. For further details, see [11][12][13][14][15][16][17][18][19][20].…”