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.