Pata contractions and coupled type fixed points

Abstract

A new coupled fixed point theorem related to the Pata contraction for mappings having the mixed monotone property in partially ordered complete metric spaces is established. It is shown that the coupled fixed point can be unique under some extra suitable conditions involving mid point lower or upper bound properties. Also the corresponding convergence rate is estimated when the iterates of our function converge to its coupled fixed point. MSC: 47H10; 34B15; 54H25

Fixed point theorems under Pata-type conditions in metric spaces

“…Coupled fixed point results under Pata-type contractive conditions were obtained by Eshaghi et al in [8]. Their basic result was the following.…”

“…The basic idea is to exploit results for mappings with one variable and apply them to mappings defined on products of spaces. We are going to apply this approach to problems with Pata-type conditions and we are going to show that better results can be obtained in this way than by a classical procedure used, e.g., in [8].…”

On Pata–Suzuki-Type Contractions

“…This theorem has been extended, modified, and generalized by several authors, e.g., [5][6][7][8][9][10][11][12][13][14][15][16].…”

Fixed Point Theorem of Ciric-Pata Type

“…In 2011, Pata [1] obtained the following result which is a generalization of the classical Banach contraction principle. Afterward many pata type fixed point theorems have been established by various authors; see ( [2], [3], [4], [5], [6], [7], [8], [9]). Particularly, Kadelburg and Radenović [7] proved some fixed point theorems of Pata type and raised the following open question on Pata-version of Ćirić contraction principle (see [10]).…”