On Fixed Point Theorems in Complete Metric Space

Abstract

In this paper, some theorems concerning the existence and uniqueness of fixed point in complete metric space are established. The results of the continuity clause we reached are introduced and some of the results we obtained are circulated.

Modify Conditions of Hardy-Rogers' Fixed Point Theorem

“…Recently, many researchers have extensively studied these types of fixed point theorems ( [4][5][6][7][8], [12][13][14][15]). Many of the concepts have been introduced recently in the Hardy-Rogers theory from those studies we mention, Rangamma [16] proved Hardy and Rogers type common fixed point theorem for a family of self-maps in cone 2-metric spaces, in the same way.…”

On Generalized Caristi Type Satisfying Admissibility Mappings

“…Newly, Isik et al [5,6] presented a new generalization of the BCP with an application, likewise, Biahdillah and Surjanto [7] introduced an application of the BCP in complexvalued Branciari b-MS, also Jleli et al [8] researched further generalizations of the BCP, and on the other hand, Patil et al [9][10][11][12] utilized the contractive, generalized contractive, Hardy-Rogers contractive, and generalized nonexpansive mappings on diferent spaces to get some new FPTs with applications.…”

New Common Uniqueness Results on Generalized Normed Space

“…Banach [1] is the first developer of this study and presented it in its basic form by presenting the Banach contraction principle, which is considered the raw material for all subsequent developments that appeared in this field. Banach proved his principle in a perfect one-dimensional space, and then more exciting results followed after that based on the development of space or the development of contraction, see ( [5], [7], [14][15][16][17][18]). In our study, we dealt with the development in space and the contraction as well.…”