Interpolative Reich–Rus–Ćirić and Hardy–Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results

Abstract

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich–Rus–Ćirić type contraction and Hardy–Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces

“…So, if we would use the chronological order for the concept we were dealing with, it should be called "Rus-Ćirić-Reich", but we adopted the alphabetical order which is usually accepted. Other combinations we can find: "Reich-Rus-Ćirić" ( [32], [45]), "Rus-Reich-Ćirić" ( [37], [40], [41]) etc.…”

Nonunique Fixed Point Results via Kannan F -Contraction on Quasi-Partial b -Metric Space

“…The concept of an F-contraction has been generalized in many directions (see, e.g., [21][22][23][24]), and as an extension, engaging work was done by many authors [25][26][27][28][29][30][31][32][33][34], which enhanced this field. In 2015, Cosentino et al [35] extended the concept of F-contraction in metric space to F-contraction in b-metric space by introducing the following condition with continuation of Definition 7.…”

New Results on Perov-Interpolative Contractions of Suzuki Type Mappings

“…Then, F has a unique fixed point in P . Afterward, this concept has been extended in different aspects for example [4][5][6][7][8][9][10][11][12][13][14] and also see e.g. [15][16][17][18][19].…”