New Fixed Point Results for Geraghty Contractions and Their Applications

Geraghty Type Contractions in Relational Metric Space with Applications to Fractional Differential Equations

“…Under the restriction Λ = , the partial order, Theorems 1 and 2 deduce the corresponding results of Zhou et al [26]. Furthermore, Theorems 1 and 2 also improve the fixed point results contained in Almarri et al [46] and Harandi and Emami [47].…”

“…This restrictive nature enables such types of results to solve many complicated real world problems occurring in fractal spaces and fractional differential equations which employ specific auxiliary conditions, e.g., [44,45]. Very recently, Almarri et al [46] established the relation-theoretic analogue of Geraghty's fixed point theorem [29], which also remains an improvement of the results of Harandi and Emami [47].…”

“…To improve the results of Almarri et al [46] by satisfying more generalized contraction conditions and to prove the existence and uniqueness results on fixed points in the framework of metric space endued with a locally S-transitive binary relation.…”

Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems

“…In contrast, Alam and Imdad [14] presented an inevitable expansion of the BCP in a complete MS provisioned with an amorphous relation. In the past few years, multiple fixed-point results have been proven involving various contractivity conditions in relational MS, e.g., [15][16][17][18][19][20][21][22] and references therein. These outcomes comprised relation-preserving contractions that continue to be weaker than the ordinary contractions, which are indeed intended to verify the relation-preserving elements only.…”

Matkowski-Type Functional Contractions under Locally Transitive Binary Relations and Applications to Singular Fractional Differential Equations

“…Subsequently, Alam and Imdad [13] investigated the coincidence and common fixed-point theorems in the framework of relational metric space. As it turns out, multiple works have already been published in the field of relational metric space by enlarging the class of relational contractions, e.g., relational Boyd-Wong contraction [14,15], relational Fcontraction [16], relational multivalued Suzuki-type θ-contraction [17], relational functional contraction [18], relational Matkowski contractions [19], relational (ψ, ϕ)-contraction [20], relational L-contraction [21], relational almost ϕ-contraction [22], and relational Geraghty contraction [23].…”