The notion of generalized almost Geraghty type contraction non-self maps in partially ordered metric spaces is introduced, and some new best proximity point theorems for this class are established. Mathematics Subject Classification: 47H10, 54H25

In this paper, we define almost Rg-Geraghty type contractions and utilize the same to establish some coincidence common fixed point results in setting of b2-metric spaces endowed with binary relations. As consequences our newly proved results, deduce for g-?-? Geraghty contraction mappings spaces. addition, derive partially ordered Moreover, show utility main provide an example application non-...

In the framework of metric spaces, we introduce concept Geraghty-Ciric type contractions and show existence uniqueness fixed point such mappings. This result improves unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) Ciric 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is Cauchy sequence. addition, two illustrative examp...

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

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