A Suzuki Type Fixed‐Point Theorem

Abstract

We present a fixed-point theorem for a single-valued map in a complete metric space using implicit relation, which is a generalization of several previously stated results including that of Suziki 2008 .

Suzuki-Type Generalization of Chatterjea Contraction Mappings on Complete Partial Metric Spaces

“…Finally, Kikkawa and Suzuki proved multivalued version of Suzuki-type results which generalize classical results of Markin [8] and Nadler [9]. For further details on this theme, one can be referred to [7,[10][11][12][13][14][15].…”

“…In this continuation, Altun and Erduran proved a Suzukitype fixed point theorem using an implicit function on complete metric space [7] wherein authors obtained unified and generalized results of Suzuki-type. Finally, Kikkawa and Suzuki proved multivalued version of Suzuki-type results which generalize classical results of Markin [8] and Nadler [9].…”

Nieto-Lopez theorems in ordered metric spaces

“…A related statement involving the Kannan type conditions [10] is to be found in Kikkawa and Suzuki [11]. For various extensions of such results we refer to Altun and Erduran [2]; see also Popescu [17]. Note that, in all these statements, the premise of the conditional contractive property (c02) is "asymmetric" with respect to the couple (x, y); so, it is natural to ask whether a supplementary condition may be added there, with a "dual" information about the variable y.…”

Suzuki-Edelstein Type Contractions via Auxiliary Functions

“…Theorems 2 and 3 are extensively studied by many authors (see, e.g., [25][26][27][28][29]). It is worth to point out that the studies mentioned above can be classified as the extensions of Banach's principle on compact/complete metric spaces, which are totally ordered.…”